Question 1

In the figure, a 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. What is the speed of the block when it has moved so that the spring is compressed to only one-half of the maximum distance?

Accepted Answer

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Question 2

A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in the figure. The vertical height above ground level at position A is 200 m. Neglect friction.  
(a) What is the total mechanical energy of the roller coaster at point A?
(b) What is the total mechanical energy of the roller coaster at point B?
(c) What is the speed of the roller coaster at point B?
(d) What is the speed of the roller coaster at point C?

Accepted Answer

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Question 3

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m)/x + (4.00 J∙m²)/x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m? A) 2.13 m/s B) 3.00 m/s C) 4.68 m/s D) 3.67 m/s

Accepted Answer

We can use conservation of mechanical energy to solve this problem. The total mechanical energy of the particle is given by: E = K + U where K is the kinetic energy and U is the potential energy. At x = 1.00 m, the particle has a kinetic energy of: K = (1/2)mv^2 = (1/2)(1.00 kg)(3.00 m/s)^2 = 4.50 J and a potential energy of: U = (-2.00 J*m)/x + (4.00 J*m*²)/x² = (-2.00 J*m)/(1.00 m) + (4.00 J*m*²)/(1.00 m*²) = 2.00 J So, the total mechanical energy at x = 1.00 m is: E = K + U = 4.50 J + 2.00 J = 6.50 J At x = 5.00 m, the potential energy of the particle is: U = (-2.00 J*m)/x + (4.00 J*m*²)/x² = (-2.00 J*m)/(5.00 m) + (4.00 J*m*²)/(5.00 m*²) = 0.20 J Therefore, the kinetic energy at x = 5.00 m is: K = E - U = 6.50 J - 0.20 J = 6.30 J and the speed is: v = ²(2K/m) = ²(2(6.30 J)/(1.00 kg)) = 3.67 m/s Therefore, the answer is D, 3.67 m/s.

Question 4

A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in the figure. The kinetic energy of the object at the origin is 12 J. The system is conservative, and there is no friction.  
(a) What will be the kinetic energy at 2.0 m along the +x-axis?
(b) What will be the speed of the object at 6.0 m along the +x-axis?

Accepted Answer

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Question 5

Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)
A) 1.24 hp
B) 2.93 hp
C) 1.86 hp
D) 0.740 hp

Accepted Answer

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Question 6

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring? A) 2.56 × 10⁵ N/m B) 3.92 × 10⁵ N/m C) 5.45 × 10⁴ N/m D) 4.12 × 10⁵ N/m E) 8.83 × 10⁴ N/m

Accepted Answer

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Question 7

A 2.0 g bead slides along a frictionless wire, as shown in the figure. At point A, the bead is moving to the right but with negligible speed.  
(a) What is the potential energy of the bead at point A?
(b) What is the kinetic energy of the bead at point B?
(c) What is the speed of the bead at point B?
(d) What is the speed of the bead at point C?

Accepted Answer

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Question 8

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.
A) 14 m/s
B) 18 m/s
C) 10 m/s
D) 9.0 m/s
E) 6.0 m/s

Accepted Answer

By conservation of energy, the potential energy at the top of the initial hill (mgh) is converted into kinetic energy at the bottom of the initial hill (1/2 mv^2), which is then conserved as the car goes up the final hill. Thus, mgh = 1/2 mv^2, where m is the mass of the car, g is the acceleration due to gravity, h is the initial height, and v is the velocity at the top of the final hill. Solving for v gives v = sqrt(2gh) = sqrt(2 x 9.81 m/s^2 x (26 m - 16 m)) = 14 m/s.

Question 9

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?
A) 26.0 m/s
B) 27.4 m/s
C) 28.7 m/s
D) 26.7 m/s
E) 28.1 m/s

Accepted Answer

The answer of A projectile is fired from ground level...

Question 10

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is  find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.
A) 13.1 m/s
B) 172 m/s
C) 9.26 m/s
D) 24.0 m/s

Accepted Answer

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Question 11

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W) A) 20.9 s B) 1.56 × 10⁴ s C) 2.18 × 10⁴ s D) 39.7 s

Accepted Answer

To find the time, we first need to calculate the power required to lift the beam and then use the power of the motor to find the time. Power (P) is defined as work done (W) per unit time (t), and work done is equal to the force applied (F) times the distance (d). Since the beam is lifted at a constant velocity, the force applied by the motor is equal to the weight of the beam (mass (m) * acceleration due to gravity (g)), and the distance is the height (h) to which the beam is lifted.$$ P = \frac{W}{t} = \frac{F \cdot d}{t} = \frac{m \cdot g \cdot h}{t} $$Given:- Mass of the beam, $m = 250 \, \text{kg}$- Height, $h = 45.0 \, \text{m}$- Acceleration due to gravity, $g = 9.81 \, \text{m/s}^2$- Power of the motor, $P = 7.08 \, \text{hp} = 7.08 \times 746 \, \text{W}$ (since $1 \, \text{hp} = 746 \, \text{W}$)First, convert horsepower to watts:$$ P = 7.08 \times 746 \, \text{W} = 5284.88 \, \text{W} $$Then, solve for time $t$:$$ t = \frac{m \cdot g \cdot h}{P} = \frac{250 \cdot 9.81 \cdot 45.0}{5284.88} \approx 20.9 \, \text{s} $$Therefore, it will take approximately 20.9 seconds for the motor to lift the beam to the height of 45.0 meters.

Question 12

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:
A) Its maximum speed will be 2v and its maximum kinetic energy will be 2K.
B) Its maximum speed will be 2v and its maximum kinetic energy will be  K.
C) Its maximum speed will be v  and its maximum kinetic energy will be 2K.
D) Its maximum speed will be 2v and its maximum kinetic energy will be 4K.
E) Its maximum speed will be 4v and its maximum kinetic energy will be 2K.

Accepted Answer

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Question 13

An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0, as shown in the figure. A very small 4.0-kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B. The tension in the rod when the ball passes through the lowest point at D is closest to 
A) 160 N.
B) 200 N.
C) 120 N.
D) 80 N.
E) 40 N.

Accepted Answer

The answer of An 8.0-m massless rod is loosely pinned...

Question 14

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction? 
A) 1.67 R
B) 2.00 R
C) 1.50 R
D) 1.33 R
E) 1.25 R

Accepted Answer

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Question 15

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?
A) 0.71 m/s
B) 4.0 m/s
C) 1.4 m/s
D) 2.8 m/s

Accepted Answer

The potential energy at the top is converted to kinetic energy at the horizontal position. Using conservation of energy: mgh = 0.5mv^2, where h = 0.1 m. Solving for v gives v = sqrt(2gh) = sqrt(2*9.8*0.1) = 1.4 m/s. However, since the rod is pivoted, the speed is doubled, giving 2.8 m/s.

Question 16

In the figure, a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0. The ball is held at point A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle with no friction and arrives at B, with the rope barely under tension. The initial velocity of the ball, at point A, is closest to 
A) 4.0 m/s
B) 5.6 m/s
C) 6.3 m/s
D) 6.9 m/s
E) 7.9 m/s

Accepted Answer

The answer of In the figure, a 4.0-kg ball is...

Question 17

If electricity costs 6.00¢/kWh (kilowatt-hour), how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?
A) $0.81
B) $0.12
C) $1.38
D) $2.27

Accepted Answer

First, convert the power of the stereo system to kilowatts: 120 W = 0.12 kW. Then, calculate the total energy used in 4 weeks (28 days): 0.12 kW * 4 hours/day * 28 days = 13.44 kWh. Finally, calculate the cost: 13.44 kWh * 6.00¢/kWh = 80.64¢, which rounds to $0.81.

Question 18

A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters above its point of release. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time? (Neglect friction and assume the spring is ideal and massless.)
A) 6.0 m
B) 12 m
C) 3.0 m
D) 48 m

Accepted Answer

The distance the dart travels is directly proportional to the square of the spring compression. Halving the compression distance results in a quarter (1/4) of the original height, so 24 meters divided by 4 equals 6 meters.

Question 19

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s? A) 99 W B) 69 W C) 138 W D) 207 W

Accepted Answer

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Question 20

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B?

Accepted Answer

The answer of It requires 6.0 J of work is...

Quiz 11: Work

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction?

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?

If electricity costs 6.00¢/kWh (kilowatt-hour) , how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s?

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B?

Quiz 11: Work

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m2) /x2. Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction?

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?

If electricity costs 6.00¢/kWh (kilowatt-hour) , how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

The work performed as a function of time for a process is given by W = at3 where a = 2.4 J/s3. What is the instantaneous power output at t = 3.7 s?

It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B?

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s?