A(n) 1100 kg car is parked on a 4◦ incline. The acceleration of gravity is 9.8 m/s 2 . Find the force of friction keeping the car from sliding down the incline.

Answer:

Electrical energy consumed, E = 1.95 × 10⁻⁵ kWh  

Explanation:

It is given that,

Power rating on the light bulb, P = 75 W

We need to find the electrical energy consumed by the bulb in 1 second of time i.e in 0.00026 hours.

[tex]P=\dfrac{energy\ consumed}{time}[/tex]

Energy consumed, E = P × t

E = 75 W × 0.00026 h

E = 0.0195 W-h

Energy consumed is calculated in kilo watt hour. Since, 1 watt = 0.001 kW

So, E = 1.95 × 10⁻⁵ kWh  

Hence, this is the required solution.

Answer:

176.4 m

Explanation:

U = 0, t = 6s, g = 9.8 m/s^2

Use second equation of motion

H = ut + 1/2 gt^2

H = 0 + 0.5 × 9.8 × 6 × 6

H = 176.4 m

It is the displacement from the point of dropping of object.

Answer:

part a)

[tex]U = 2\times 10^9 J[/tex]

Part b)

[tex]m = 5.6 \times 10^3 kg[/tex]

Part c)

Huge damage will be there in tree

Explanation:

Part a)

Energy loss due to charge flow through given potential difference is given as

[tex]U = qV[/tex]

now plug in all the values in it

[tex]U = (20 C)(1.00 \times 10^2 \times 10^6 V)[/tex]

[tex]U = 2\times 10^9 J[/tex]

Part b)

Now this energy is used to raise the temperature of water from 15 degree C to boiling point

So here we will have

[tex]Q = ms\Delta T[/tex]

[tex]2 \times 10^9 = m(4186)(100 - 15)[/tex]

[tex]m = 5.6 \times 10^3 kg [/tex]

Part c)

Since in part b) we can say its a huge amount of water that will boil due to the amount of energy that strikes to the tree.

So it will make huge damage to the tree

Final answer:

A lightning bolt moving 20.0 C of charge through a potential difference of 1.00 × 10² MV dissipates 2.00 × 10¹ joules of energy. This energy can boil a significant mass of water, demonstrating the power of lightning. The rapid boiling of sap and expansion of steam can cause the tree to explosively splinter.

Explanation:

Understanding the Physics of a Lightning Strike on a Tree

A lightning bolt striking a tree involves complex physical phenomena, including the movement of charge and the dissipation of significant amounts of energy. When a lightning bolt with 20.0 C of charge passes through a potential difference of 1.00 × 10² MV, we can calculate the energy dissipated using the relationship between charge, potential difference, and energy.

(a) Calculating Dissipated Energy:

The energy dissipated can be calculated using the formula E = QV, where E is the energy in joules, Q is the charge in coulombs, and V is the potential difference in volts. Given the charge (20.0 C) and the potential difference (1.00 × 10² MV or 1.00 × 10¸ V), the energy dissipated is 2.00 × 10¹ joules (or 2 billion joules).

(b) Heating and Boiling Water with This Energy:

To determine what mass of water could be raised from 15°C to the boiling point and then boiled, we need to consider the specific heat capacity of water and the latent heat of vaporization. However, without diving into specific calculations here, it's clear that the energy amount is sufficient to boil a significant mass of water, showcasing the tremendous power of lightning.

(c) Potential Damage to the Tree:

The sudden energy release and the boiling of sap inside the tree can cause severe damage. The rapid expansion of steam may result in the explosive splintering of the tree trunk, a common effect seen in trees struck by lightning.

(a) The impulse delivered to the ball by the racket is 5.24 kg.m/s

(b) The work that the racket does on the ball is -35.1 Joule

Given :

mass of ball = m = 0.06 kg

initial velocity = v₁ = -50.4 m/s

final velocity = v₂ = 37.0 m/s

Unknown :

(a) Impulse = I = ?

(b) Work = W = ?

Solution :

In this question , we could use the formula from Second Law of Newton :

[tex]I = \Delta p[/tex]

[tex]I = p_2 - p_1[/tex]

[tex]I = m \times v_2 - m \times v_1[/tex]

[tex]I = m \times (v_2 - v_1)[/tex]

[tex]I = 0.06 \times (37.0 - (-50.4))[/tex]

[tex]I = 0.06 \times (87.4)[/tex]

[tex]I = 5.244~kg.m/s[/tex]

[tex]\large { \boxed {I \approx 5.24~kg.m/s} }[/tex]

[tex]W = F \times d[/tex]

[tex]W = (\frac{I}{\Delta t})(\frac {v_1 + v_2}{2} \Delta t)[/tex]

[tex]W = \frac{I(v_1 + v_2)}{2}[/tex]

[tex]W = \frac{5.244(-50.4 + 37)}{2}[/tex]

[tex]W = \frac{5.244(-13.4)}{2}[/tex]

[tex]W = -35.1348~Joule[/tex]

[tex]\large { \boxed {W \approx -35.1~Joule}}[/tex]

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Grade: High School

Subject: Physics

Chapter: Dynamics

Keywords: Newton, Law, Impulse, Work

In this physics problem, we calculate the impulse delivered by the racket to the tennis ball and the work done by the racket on the ball.

The impulse delivered to the ball by the racket:

The work done by the racket on the ball:

Answer:

28.2 m/s

Explanation:

The range of a projectile launched from the ground is given by:

[tex]d=\frac{v^2}{g}sin 2\theta[/tex]

where

v is the initial speed

g = 9.8 m/s^2 is the acceleration of gravity

[tex]\theta[/tex] is the angle at which the projectile is thrown

In this problem we have

d = 81.1 m is the range

[tex]\theta=45^{\circ}[/tex] is the angle

Solving for v, we find the speed of the projectile:

[tex]v=\sqrt{\frac{dg}{sin 2 \theta}}=\sqrt{\frac{(81.1 m)(9.8 m/s^2)}{sin (2\cdot 45^{\circ})}}=28.2 m/s[/tex]

Answer:

The ball to hit the ground in 0.53 s.

Explanation:

Given that,

Height = 1.4 m

Time t = 0.53 s

Initial speed = 35 m/s

We need to calculate the time when the ball to hit the ground

Using equation of motion

[tex]s_{y}=u_{y}t-\dfrac{1}{2}gt^2+h_{0}[/tex]

Where, s= vertical height

u= vertical velocity

t = time

h = height

Put the value in equation

[tex]0=0-\dfrac{1}{2}\times9.8\times t^2+1.4[/tex]

[tex]t^2=\dfrac{1.4}{4.9}[/tex]

[tex]t=\sqrt{\dfrac{1.4}{4.9}}[/tex]

[tex]t=0.53\ s[/tex]

Hence, The ball to hit the ground in 0.53 s.

Final answer:

A baseball thrown horizontally with an initial speed will take the same amount of time to fall as a dropped object from the same height, which is 0.53 seconds, because the horizontal speed does not affect the vertical fall time.

Explanation:

The time it takes for an object to fall from a height solely depends on the force of gravity and the initial vertical speed. Since the baseball is thrown horizontally with an initial speed of 35 m/s, this speed does not affect the vertical fall time. The ball will hit the ground in the same duration as any object dropped from the same height without any initial vertical velocity, provided that air resistance is negligible. The previously stated object took 0.53 s to fall from a height of 1.4 m, therefore the baseball will also take 0.53 seconds to hit the ground.

Answer:

B

Explanation:

Use conservation of momentum: Total momentum of the system before is the same as the total momentum after the collision. Since both are moving north, the momentum of both cars is in the same direction, and the total momentum before collision is 1000kg*20m/s + 1500kg*36m/s = 74000kg-m/s.

This is the same amount of momentum after collision, and since they are locked together, their mass is added. The velocity can be found by: 74000kg-m/s ÷ 2500kg = 29.6m/s.

momentum = mass*velocity

The velocity of the two cars combined, immediately after the collision, can be determined by conserving the total momentum before the collision. This velocity is 29.6 m/s north.

This problem is about the conservation of momentum in a collision. Momentum before the collision is the total of the momentum of the two cars combined. We can calculate this using the formula 'momentum = mass x velocity'. For the 1000-kg car it's (1000 kg)x(20 m/s) = 20000 kg.m/s and for the 1500-kg car, it's (1500 kg)x(36 m/s) = 54000 kg.m/s. The total momentum before the collision is 20000 + 54000 = 74000 kg.m/s.

After the collision, the two cars move together, meaning the total mass is now 1000 + 1500 = 2500 kg. The question asks for the velocity (v) of the cars immediately after the collision. As the total momentum must be conserved, we can find this velocity using the formula 'momentum = total mass x velocity'. So, 74000 = (2500 kg) x v. To solve for v, we divide 74000 by 2500. Doing this gives v = 29.6 m/s. Therefore, the velocity of the cars immediately after the collision is 29.6 m/s north.

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(a) 252 N, opposite to the applied force

There are two forces acting on the refrigerator in the horizontal direction:

- the pushing force of 252 N, F, forward

- the frictional force, Ff, pulling backward

In this case, the refrigerator is not moving: this means that its acceleration is zero. According to Newton's second law, this also means that the net force acting on the refrigerator is also zero:

[tex]\sum F = ma = 0[/tex]

So we have

[tex]F-F_f = 0[/tex]

which means that the frictional force is equal in magnitude to the pushing force:

[tex]F_f = F = 252 N[/tex]

and the direction is opposite to the pushing force.

(b) 334.8 N

The force that must be applied to the refrigerator to make it moving is equal to the maximum force of friction, which is given by:

[tex]F_{max} = \mu mg[/tex]

where

[tex]\mu = 0.61[/tex] is the coefficient of static friction

m = 56 kg is the mass of the refrigerator

g = 9.8 m/s^2 is the acceleration of gravity

Substituting:

F_max = (0.61)(56 kg)(9.8 m/s^2)=334.8 N

The force that will move the object is 83 N in the negative x direction.

The frictional force is the force that opposes motion. The force of friction acts in the opposite direction to the force that is moving the object. Now we can obtain the frictional force from;

μs = F/mg

F = μsmg = 0.61 * 56 kg * 9.8 m/s^2 = 335 N (positive  direction)

Secondly;

ma = F - Ff

Where;

ma = resultant force

F = moving force

Ff = frictional force

Now we need to find the net force ma

ma = 252 N - 335 N

ma = -83 N

The force that will move the object is 83 N in the negative x direction.

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The tension in the rod as the stone moves through the bottom of the circle is 80 N, which is found by applying the principles of conservation of energy and circular motion.

The problem involves the concept of centripetal force and the principle of conservation of energy. When the stone is at the bottom of the circular path, the centripetal force necessary to keep it moving in a circle is provided by the tension, T in the rod and the weight of the stone. The tension can be calculated using the formula for the centripetal force, which is F = m * g + m * v²/r where m is the mass of the stone (2 kg), g is the acceleration due to gravity (approximate 10 m/s²), v is the velocity of the stone and r is the radius of of the circle.

Since the energy at the top of the circle (potential energy) is equal to the energy at the bottom of the circle (kinetic energy + potential energy), and we know that potential energy = m * g * h and kinetic energy = 1/2 * m * v², we can solve for v² = 2 * g * h. Hence, substituting v² in the previous formula, we get T = m * g + m * (2 * g * h)/r. Considering that h=r=1.2m, this simplifies to T = 4 * m * g , which, when evaluated equals 80N. Therefore, the correct answer is (d) 80 N.

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The minimum speed of an object in simple harmonic motion occurs when it is at the equilibrium point. Hence the correct answer is option B

In simple harmonic motion, the minimum speed of an object occurs when it is at the equilibrium point. The equilibrium position is where the object would naturally rest in the absence of force. When the object is at the equilibrium point, it has zero acceleration and the speed is at its minimum.

Hence the correct answer is option B

Answer:

The current in any one of the resistors is 1 A.

Explanation:

It is given that, four 20 ohm resistors are connected in parallel. In parallel combination of resistors, the voltage across each and every resistor is same while the current divides. The equivalent resistance of all resistors is given by :

[tex]\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+\dfrac{1}{R_4}[/tex]

[tex]\dfrac{1}{R_{eq}}=\dfrac{1}{20\ \Omega}+\dfrac{1}{20\ \Omega}+\dfrac{1}{20\ \Omega}+\dfrac{1}{20\ \Omega}[/tex]

[tex]R_{eq}=5\ \Omega[/tex]

Current flowing in the entire circuit can be calculated using Ohm's law as :

Current, [tex]I=\dfrac{V}{R_{eq}}[/tex]

[tex]I=\dfrac{20\ V}{5\ \Omega}[/tex]

I = 4 A

Since, in parallel combination current divides. So, current flowing in all four resistor divides and is 1 A. Hence, this is the required solution.

The current in a single 20 Ohm resistor connected in parallel to a 20 V emf device is 1 A. This is calculated using Ohm's law (I = V/R).

The question involves calculating the current in a single resistor when four 20 Ohm resistors are combined in parallel and connected to a 20 V emf device. For resistors in parallel, they share the same potential difference, or voltage. In this case, the emf device provides each parallel resistor with a potential difference of 20 V.

By using Ohm's law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points, the current can be calculated. Ohm's law is typically represented by the formula I = V/R, where I is the current, V is the voltage, and R is the resistance. In this scenario, we can calculate the current as I = 20V/20Ohm which equals 1 A.

So, the current that will flow through any one of the 20 Ohm resistors connected in parallel and connected to a 20 V power supply would be 1 A. The correct answer falls outside the options given and is 1 A.

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Answer:

0.25 m/s

Explanation:

This problem can be solved by using the law of conservation of momentum - the total momentum of the squid-water system must be conserved.

Initially, the squid and the water are at rest, so the total momentum is zero:

[tex]p_i = 0[/tex]

After the squid ejects the water, the total momentum is

[tex]p_f = m_s v_s + m_w v_w[/tex]

where

[tex]m_s = 1.60 kg[/tex] is the mass of the squid

[tex]v_s[/tex] is the velocity of the squid

[tex]m_2 = 0.115 kg[/tex] is the mass of the water

[tex]v_w = 3.50 m/s[/tex] is the velocity of the water

Due to the conservation of momentum,

[tex]p_i = p_f[/tex]

so

[tex]0=m_s v_s + m_w v_w[/tex]

so we can find the final velocity of the squid:

[tex]v_s = -\frac{m_w v_w}{m_s}=-\frac{(0.115 kg)(3.50 m/s)}{1.60 kg}=-0.25 m/s[/tex]

and the negative sign means the direction is opposite to that of the water.

By applying the conservation of momentum, the squid would achieve a speed of about 0.80 m/s in the opposite direction to that of the ejected water.

This problem is related to the principle of conservation of momentum. According to this principle, the total momentum before and after the ejection of the water should be the same, because no external force is acting on this system of the squid and the water it ejects.

The initial momentum of the system is 0, because the squid is initially stationary. When the squid ejects water, it gets a momentum in the opposite direction. Hence,

0 = momentum of squid + momentum of water

or, 0 = (mass of squid × speed of squid) + (mass of ejected water × speed of ejected water),

Solving this equation for the speed of the squid gives:

speed of squid = - (mass of ejected water × speed of ejected water) / mass of squid

Substituting the given values into this equation:

speed of squid = - (0.115 kg × 3.50 m/s) / 1.60 kg ≈ -0.80 m/s.

The negative sign indicates that the squid moves in the opposite direction to that of the ejected water.

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This is true. The victim could be too embarrassed and would not want others to know because people could bash her for that.

If a victim of sexual harassment asks a supervisor not report it, the supervisor should respect his or her wishes is False.

If a victim of sexual harassment asks a supervisor not to report it, the supervisor should not automatically respect their wishes. It is essential to prioritize the safety and well-being of the victim and address the issue appropriately.

Sexual harassment is a serious and unlawful matter, and supervisors have a legal and ethical obligation to address and report such incidents following company policies and the law.

Reporting incidents of sexual harassment is crucial for investigating the matter, providing support to the victim, and taking appropriate actions to prevent further harassment and protect the well-being of employees.

Supervisors should follow their organization's policies and procedures for handling harassment complaints and ensure that victims are treated with sensitivity and respect throughout the process. Confidentiality should be maintained to the extent possible, but it should not prevent the necessary actions to address and resolve the issue effectively.

Hence, If a victim of sexual harassment asks a supervisor not report it, the supervisor should respect his or her wishes is False.

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Answer:

Yes

Explanation:

The velocity measured by Jennifer and Johnny is

[tex]v_m = 34.87 m/s[/tex]

The actual velocity is

[tex]v=34.15 m/s[/tex]

We can calculate the % error of the students measurement as follows:

[tex]Err = \frac{v_m - v}{v}\cdot 100 = \frac{34.87 m/s-34.15 m/s}{34.15 m/s}\cdot 100 =0.021 \cdot 100 = 2.1 \%[/tex]

Which is lower than the 2.5% maximum error required, so the two students will pass the test.

Final answer:

Jennifer and Johnny's measurement has a percentage error of approximately 2.11%, which is less than the maximum allowed error of 2.5%. Therefore, they will pass their final project.

Explanation:

To determine if Jennifer and Johnny passed their final project, we need to calculate the percentage error of their measured velocity. The percentage error is calculated using the formula:

Percentage Error = |(Actual Value - Experimental Value) / Actual Value| × 100%

First, let's find the absolute difference between the actual velocity (34.15 m/s) and the measured velocity (34.87 m/s):

|34.15 m/s - 34.87 m/s| = |(-0.72 m/s)| = 0.72 m/s

Now, we calculate the percentage error:

Percentage Error = (0.72 m/s / 34.15 m/s) × 100% ≈ 2.11%

Since the percentage error they obtained (2.11%) is less than the maximum allowed error of 2.5%, Jennifer and Johnny will pass their final project.

Answer:

1.637687 x 10¹³ m²

Explanation:

Land area of Russia has been given in the question as

A = land area of Russia = 16,376,870  km²

we know that

1 km = 1000 m

hence

A = land area of Russia = 16,376,870  (1000 m)² = 16,376,870,000,000 m²

A = 16,376,870,000,000 m²

To represent the area in exponent form, we shift the decimal place from right to left until we have one decimal place.

So we get

A = 1.637687 x 10¹³ m²

Answer:

The correct answer is :A and C

Explanation:

According to the rule

1- Zeroes at the beginning of a number are never significant.

2- Zeroes at the end of a number are significant if there is a decimal point.

(a) 0.00012 s and 12000 s

0.00012 has 2 significant figure and 12000 has 2 significant figures

(b) 11.0 m and 11.00 m

11.0 has 3 significant figures and 11.00 has 4 significant figure.

(c)  0.0250 m and 0.205

0.0250 has 3 significant figure and 0.250 has 3 significant figures

(d) 250.0 L and 2.5×10−2L

250.0 has 4 significant figures and 2.5x10−2 has 2 sig figures.

So (a) and (c) pairs have same number of sig figures.

Final answer:

The pair out of the provided options that contains the same number of significant figures is 0.0250 m and 0.205 m, both with three significant figures.

Explanation:

When comparing significant figures in different numbers, we must apply the rules for determining the number of significant figures to each number.

0.00012 s has two significant figures (the leading zeros are not significant).

12000 s likely has two significant figures (unless further decimal places are indicated or if it's written in scientific notation, such as 1.2×10⁴ which would have three significant figures).

11.0 m and 11.00 m have three and four significant figures respectively (trailing zeros after a decimal are significant).

0.0250 m has three significant figures (leading zeros are not significant, but trailing zeros after a decimal are).

0.205 m has three significant figures (leading zeros are not significant).

250.0 L has four significant figures (trailing zeros after a decimal are significant).

2.5×10⁻² L has two significant figures (in scientific notation, all digits are significant).

Therefore, the pairs that contain the same number of significant figures are 0.0250 m and 0.205 m, both with three significant figures.

Answer:

335°C

Explanation:

Heat gained or lost is:

q = m C ΔT

where m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.

Heat gained by the water = heat lost by the copper

mw Cw ΔTw = mc Cc ΔTc

The water and copper reach the same final temperature, so:

mw Cw (T - Tw) = mc Cc (Tc - T)

Given:

mw = 390 g

Cw = 4.186 J/g/°C

Tw = 22.6°C

mc = 248 g

Cc = 0.386 J/g/°C

T = 39.9°C

Find: Tc

(390) (4.186) (39.9 - 22.6) = (248) (0.386) (Tc - 39.9)

Tc = 335

Data obtained from the question

Mass of copper (M꜀) = 248 g

Volume of water  = 390 mL

Density of water = 1 g/mL

Initial temperature of water (Tᵥᵥ) = 22.6 °C

Equilibrium temperature (Tₑ) = 39.9 °C

Determination of the mass of water

Volume of water = 390 mL

Density of water = 1 g/mL

[tex]Density = \frac{mass}{volume}\\\\1 = \frac{mass}{390}[/tex]

Cross multiply

[tex]Mass = 1 * 390[/tex]

Determination the initial temperature of the copper.

Mass of copper (M꜀) = 248 g

Mass of water (Mᵥᵥ) = 390 g

Initial temperature of water (Tᵥᵥ) = 22.6 °C

Equilibrium temperature (Tₑ) = 39.9 °C

1. Specific heat capacity of water (Cᵥᵥ) = 4.184 J/gºC

2. Specific heat capacity of copper (C꜀) = 0.385 J/gºC

Heat lost by copper = heat gained by water

[tex]Q_{c} = Q_{w} \\ \ M_{c} C_{c}(T_{c}-T_{e}) = M_{w} C_{w}(T_{e}-T_{w})\\248* 0.385(T_{c}-39.9) = 390*4.184(39.9-22.6)\\95.48(T_{c}-39.9) = 1631.76*17.3\\95.48(T_{c}-39.9) = 28229.448[/tex]

Divide both side by 95.48

[tex]T_{c} - 39.9 = \frac{28229.448}{95.48}\\T_{c} - 39.9 = 295.658[/tex]

Collect like terms

[tex]T_{c} = 295.658 + 39.9[/tex]

Therefore, the initial temperature of the piece of copper is 335.6 °C.

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Answer:

No, it is not correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source.

Explanation:

While Doppler Effect is due to motion of the source or observer but it is not the apparent change in the speed of the wave. The speed of the wave remains the same. It is the wavelength and frequency of the waves that change in Doppler Effect when there is a relative motion between source and observer.

The Doppler Effect is the change in frequency, not speed, of a wave due to the relative motion between the source and observer.

It would not be correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source. The Doppler Effect actually refers to the apparent change in the frequency of a wave as a result of the relative motion between the source of the wave and the observer. While the speed of the wave itself remains constant, the wavelength experienced by the observer can either compress or stretch depending on whether the source is moving towards or away from them, thereby changing its perceived frequency.

Answer:

The angular acceleration is [tex]0.209\ rad/s^2[/tex]

Explanation:

Given that,

Angular velocity, [tex]\omega_{i} = 30.0\ rpm[/tex]

Angular velocity, [tex]\omega_{f} = 50.0\ rpm[/tex]

Time t = 10.0 sec

We need to calculate the angular acceleration

Using formula of angular acceleration

[tex]\alpha=\dfrac{\Delta \omega}{\Delta t}[/tex]

[tex]\alpha=\dfrac{\omega_{f}-\omega_{i}}{\Delta t}[/tex]

[tex]\alpha=\dfrac{50.0-30.0}{10.0}[/tex]

Now, we change the angular velocity in rad/s.

[tex]\omega=20\times\dfrac{2\pi}{60}[/tex]

[tex]\omega=2.09\ rad/s[/tex]

[tex]\alpha=\dfrac{2.09}{10.0}[/tex]

[tex]\alpha=0.209\ rad/s^2[/tex]

Hence, The angular acceleration is [tex]0.209\ rad/s^2[/tex]

Answer:

The rate of angular acceleration is 0.209 rad/s²

Explanation:

the solution is in the attached Word file

Answer:

Upward

Explanation:

For charged particles immersed in an electric field:

- if the particle is positively charged, the direction of the force is the same as the direction of the electric field

- if the particle is negatively charged, the direction of the force is opposite to the direction of the electric field

In this problem, we have an electron - so a negatively charged particle - so the direction of the force is opposite to that of the electric field.

Since the electric field is directed downward, therefore, the electric force on the electron will be upward.

(a) [tex]4.14 rad/s^2[/tex]

The relationship beween centripetal acceleration and angular speed is

[tex]a=\omega^2 r[/tex]

where

[tex]\omega[/tex] is the angular speed

r is the radius of the circular path

Here we gave

[tex]a = 9g = 88.2 m/s^2[/tex] is the centripetal acceleration

r = 5.15 m is the radius

Solving for [tex]\omega[/tex], we find:

[tex]\omega = \sqrt{\frac{a}{r}}=\sqrt{\frac{88.2 m/s^2}{5.15 m}}=4.14 rad/s^2[/tex]

(b) 21.3 m/s

The relationship between the linear speed and the angular speed is

[tex]v=\omega r[/tex]

where

v is the linear speed

[tex]\omega[/tex] is the angular speed

r is the radius of the circular path

In this problem we have

[tex]\omega=4.14 rad/s[/tex]

r = 5.15 m

Solving the equation for v, we find

[tex]v=(4.14 rad/s)(5.15 m)=21.3 m/s[/tex]

Explanation:

(a) Centripetal acceleration, [tex]a=9g=88.2\ m/s^2[/tex]

Radius, r = 5.15 m

Let [tex]\omega[/tex] is the angular speed. The relation between the angular speed and angular acceleration is given by :

[tex]a=\omega^2 r[/tex]

[tex]\omega=\sqrt{\dfrac{a}{r}}[/tex]

[tex]\omega=\sqrt{\dfrac{88.2}{5.15}}[/tex]

[tex]\omega=4.13\ rad/s[/tex]

(b) Let v is the linear speed of the person in the centrifuge have at this acceleration. It is given by :

[tex]v=r\times \omega[/tex]

[tex]v=5.15\times 4.13[/tex]

v = 21.26 m/s

Hence, this is the required solution.

Probably not. The elevator has security system just like any device. It will automatically trigger breaks in case it detects some sort of free fall.

Person inside free falling elevator could experience 0G or no gravity effect something similar to what astronauts experience in earth's orbit.

The only damage that could happen to you is when the breaks are released you won't feel 0G anymore and fall about 4ft to the floor of the elevator.

Hope this helps.

r3t40

The time it takes a beam of light to get from the Sun to the Earth is [tex]4.99\times 10^2secs[/tex]

The formula for calculating the average speed is expressed according to the formula:

[tex]Speed= \frac{distance}{time}[/tex]

Given the speed of light as [tex]3.0 \times 10^8m/s[/tex]

Distance from earth to the sum is [tex]149.6\times 10^9m[/tex]

Substitute the given parameters into the formula to get the time "t"

[tex]t=\frac{d}{t} \\t=\frac{149.6\times10^9m}{3.0\times10^8}\\t=49.87\times 10\\t =498.7secs[/tex]

Hence the time it takes a beam of light to get from the Sun to the Earth is [tex]4.99\times 10^2secs[/tex]

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Answer:

[tex]P_1 - P_2 = 2295 pascal[/tex]

Explanation:

As we know by Bernoulli's principle

[tex]P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2[/tex]

[tex]P_1 - P_2 = \frac{1}{2}\rho v_2^2 - \frac{1}{2} \rho v_1^2[/tex]

here we know that

[tex]\rho = 1000 kg/m^3[/tex]

also we know that

[tex]v_1 = 2.1 m/s[/tex]

[tex]v_2 = 3 m/s[/tex]

now we have

[tex]P_1 - P_2 = \frac{1}{2}(1000)(3.0^2 - 2.1^2)[/tex]

[tex]P_1 - P_2 = 2295 pascal[/tex]

To find the pressure difference between two points in a pipe, we can use Bernoulli's equation. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid remains constant along a streamline.

To find the pressure difference between two points in a pipe, we can use Bernoulli's equation. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid remains constant along a streamline. In this case, since the pipe is horizontal and we neglect friction, the potential energy term can be ignored. So we are left with:

P1 + 1/2ρv12 = P2 + 1/2ρv22

Where P1 and P2 are the pressures at the entrance and exit respectively, ρ is the density of the fluid, and v1 and v2 are the velocities at the entrance and exit respectively.

Using the given values, we can calculate the pressure difference.

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The style of parenting is most likely to produce self indulgent children who have little self control.

A biological parent is the person who contributed to the child's genes, and in the case of the mother, carried the child during a pregnancy. A biological parent can, but doesn't have to be a legal guardian of the child.

An adoptive parent is did not directly contribute to the  child's genes, but took over the care of the child after the child's birth. An adoptive parent is always a legal guardian of the child and maintains the contact with the child after their maturity.

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Answer: v= 160ft/s

a=32ft/s^2 constant

Explanation:

s(t)=400-16t^2 derivative of position is velocity v(t) and derivative of velocity is acceleration a(t) so let s(t)=0 to find the time of flight to reach the ground and take the two derivatives and use the time found and solve. Also acceleration is a constant as it’s gravity.

0=400-16t^2

400=16t^2

25=t^2

t=5s

ds/dt=v(t)=0-32t

dv/dt=a(t)=-32 constant(gravity)

v(t)=-32(5s)= -160ft/s negative sign is only showing direction

The velocity of the object the moment it reaches the ground is 160 ft/s.

The problem can be solved by following steps.

s(t) = 400-16t^2 (given)

Let s(t)=0

Therefore

0= 400-16t^2

400=16t^2

25=t^2

Therefore

t = 5sec

Now as we know that the derivative of the position is Velocity

so v(t) = ds/dt = -32t

where t = 5sec

substitute the value of t in v(t)

Therefore, v(t) = -32(5) = -160

The direction is negative

Hence the velocity is 160ft/s

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Answer:

The charge passing through a battery is [tex]1.22\times10^{5}\ C[/tex].

Explanation:

Given that,

Current = 7.2 A

Time = 4.7 hours

We need to calculate the charge

The charge is the product of current and time.

Using formula of charge

[tex]Q=it[/tex]

Where, Q = charge

i = current

t = time

Put the value into the formula

[tex]Q=7.2\times4.7\times3600[/tex]

[tex]Q=1.22\times10^{5}\ C[/tex]

Hence, The charge passing through a battery is [tex]1.22\times10^{5}\ C[/tex].

Answer:

The speed of the satellite is 7809.52 m/s        

Explanation:

It is given that,

Radius of Earth, [tex]r=6.38\times 10^6\ m[/tex]

Mass of earth, [tex]M=5.98\times 10^{24}\ kg[/tex]

A satellite moves in a circular orbit a distance of, [tex]d=1.6\times 10^5\ m[/tex]  above Earth's surface.

We need to find the speed of the satellite. It is given by :

[tex]v=\sqrt{\dfrac{GM}{R}}[/tex]

R = r + d

[tex]R=(6.38\times 10^6\ m+1.6\times 10^5\ m)=6540000\ m[/tex]

So, [tex]v=\sqrt{\dfrac{6.67\times 10^{-11}\ Nm^2/kg^2\times 5.98\times 10^{24}\ kg}{6540000\ m}}[/tex]

v = 7809.52 m/s

So, the speed of the satellite is 7809.52 m/s. Hence, this is the required solution.

you use the formula F=ma to get the answer

Answer:

-220 rad/s²

Explanation:

ω² = ω₀² + 2α(θ - θ₀)

We're given that ω = 0 rev/min, ω₀ = 3700 rev/min, and θ - θ₀ = 54.0 rev.

Converting to rad/s:

0 rev/min × (2π rad / rev) × (1 min / 60 s) = 0 rad/s

3700 rev/min × (2π rad / rev) × (1 min / 60 s) = 123⅓π rad/s

54.0 rev × (2π rad / rev) = 108π rad

Plugging in:

(0 rad/s)² = (123⅓π rad/s)² + 2α(108π)

α = -221.2 rad/s²

There's 2 significant figures in 3700 rev/min, so we need to round our answer to 2 sig figs.  The angular acceleration is -220 rad/s².