Q: A crate of mass 8.0 kg is pushed up a 2.5 m ramp inclined at $$30^\circ$$ with an initial speed of 5.0 m/s. If it slides 1.6 m up before stopping, what is the magnitude of the friction force?

$$f = \frac{\frac{1}{2} m v^2$ - m g s \sin \theta}{-s}$$

Question 1

A block of mass $$m$$ slides down a frictionless curved ramp from a height $$h$$ and reaches the bottom with speed $$v. $$Which of the following equations correctly relates the gravitational potential energy lost to the kinetic energy gained by the block?

Accepted Answer

$$mgh = \frac{1}{2}mv^2$

Question 2

A 25.0 kg skateboarder starts from rest at the top of a frictionless quarter-circle ramp of radius $$R = 3.00 m. $$What is his speed at the bottom of the ramp?

Accepted Answer

$$v = \sqrt{2gR}$$

Question 3

Using the result $$v = \sqrt{2gR}$$, what is the numerical value of the skateboarder's speed at the bottom if $$g = 9.8 m/s$^2$$ and $$R = 3.00 m$$?

Accepted Answer

$$7.67 m/s$$

Question 4

At the bottom of the ramp, what is the normal force acting on the skateboarder of mass $$m$$ moving at speed $$v$$ along a curve of radius $$R$$?

Accepted Answer

$$N = m\left(\frac{v^2$}{R} + g\right)$$

Question 5

A 350 kg roller coaster starts from rest at a height of 25 m and descends to a height of 12 m on a frictionless track. What is its speed at the lower point?

Accepted Answer

$$v = \sqrt{2g(25-12)}$$

Question 6

A 2000 kg elevator falls at 8.00 m/s and is stopped by a spring compressed 3.00 m. Ignoring friction, what is the required spring constant $$k$$?

Accepted Answer

$$k = \frac{m v^2$ + 2 m g x}{x^2$}$$

Question 7

Which of the following statements about conservative forces is NOT true?

Accepted Answer

The work done by a conservative force depends on the path taken.

Question 8

A crate of mass 8.0 kg is pushed up a 2.5 m ramp inclined at $$30^\circ$$ with an initial speed of 5.0 m/s. If it slides 1.6 m up before stopping, what is the magnitude of the friction force?

Accepted Answer

$$f = \frac{\frac{1}{2} m v^2$ - m g s \sin 	heta}{-s}$$

Question 9

A block is released from rest on a frictionless incline and compresses a spring at the bottom. While the block is compressing the spring, what happens to the gravitational and elastic potential energies?

Accepted Answer

Gravitational potential energy decreases; elastic potential energy increases.

Question 10

Which of the following best describes the work done by friction as a car tire flexes while rolling?

Accepted Answer

It is a nonconservative force, converting mechanical energy into internal energy.

Question 11

Two blocks, $$m_1$$ and $$m_2$$, are connected by a rope over a pulley. $$m_1$$ slides down a frictionless ramp while $$m_2$$ moves upward. After each block has moved a distance $$d$$, the total work done on $$m_1 is$$:

Accepted Answer

The same as the total work done on $$m_2.$$

Question 12

Which path requires the most energy for a car to travel from the base to the summit of a mountain, assuming only gravity acts and all paths have the same vertical height?

Accepted Answer

All paths require the same energy.

Question 13

A block of mass $$m is $$released from rest at height $$h on $$two different frictionless ramps (one straight, one curved) with the same vertical drop. Which block arrives at the bottom with greater speed?

Accepted Answer

Both blocks arrive with the same speed.

Question 14

The area under the force vs. displacement graph for a spring stretched from $$x = 0 to$$ $$x = X$$ represents:

Accepted Answer

The work done on the spring, $$W = \frac{1}{2}kX^2$

Question 15

Which of the following is the correct expression for average power $$P_{av}$$ during a time interval $$\Delta t$$?

Accepted Answer

$$P_{av} = \frac{\Delta W}{\Delta t}$$

Question 16

A person lifts a 10 kg box vertically upward 2 m in 4 s. What is the average power output?

Accepted Answer

$$P = \frac{mgh}{t} = \frac{10 	imes 9.8 	imes 2}{4} = 49 W$$

Guided Study: Energy Conservation and Forces on a Curved Ramp

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