Q: A particle slides down a frictionless incline from a height $$h$$, then moves across a rough horizontal surface (coefficient of kinetic friction $$\mu_k = 0.5) of $$length $$d$$, and finally enters a smooth semicircular track of radius $$R. If $$the particle loses contact with the track at an angle $$\theta$$ from the vertical, which equation correctly relates $$d$$ and $$R$$?

$$d = \dfrac{2R(1 - \cos\theta)}{\mu_k}$$

Question 1

A particle slides down a frictionless incline from a height $$h$$, then moves across a rough horizontal surface (coefficient of kinetic friction $$\mu_k = 0.5) of $$length $$d$$, and finally enters a smooth semicircular track of radius $$R. If $$the particle loses contact with the track at an angle $$	heta$$ from the vertical, which equation correctly relates $$d$$ and $$R$$?

Accepted Answer

$$d = \dfrac{2R(1 - \cos	heta)}{\mu_k}$$

Question 2

Which of the following is a conservative force?

Accepted Answer

Gravitational force

Question 3

A block of mass $$m$$ slides down a frictionless incline and then moves across a rough horizontal surface. The work done by friction is given by which equation?

Accepted Answer

$$W_{fric} = \mu_k m g d$$

Question 4

If a particle loses contact with a smooth circular track at angle $$	heta$$ from the vertical, what is the normal force at that point?

Accepted Answer

$$N = 0$$

Question 5

Which statement best describes the work done by a conservative force?

Accepted Answer

It depends only on the initial and final positions.

Question 6

A particle of mass $$m$$ starts from rest at height $$h$$ and slides down to the bottom of a frictionless incline. What is its speed at the bottom?

Accepted Answer

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

Question 7

Which of the following is NOT a non-conservative force?

Accepted Answer

Gravitational force

Question 8

The kinetic energy theorem states that the net work done on an object is equal to:

Accepted Answer

The change in kinetic energy

Question 9

A block slides down a rough incline and comes to rest after traveling a distance $$d. If $$the coefficient of kinetic friction is $$\mu_k$$, what is the total work done by friction?

Accepted Answer

$$W = -\mu_k m g d$$

Question 10

Which of the following best describes the energy transformation as a particle slides down a frictionless incline and then across a rough surface?

Accepted Answer

Potential energy is converted to kinetic energy, then partially to thermal energy due to friction.

Question 11

A particle moves in a circular path of radius $$R$$ with speed $$v. $$What is the required centripetal force?

Accepted Answer

$$F_c = m v^2$ / R$$

Question 12

Which of the following is true about the work done by the normal force on a particle moving along a surface?

Accepted Answer

It is always zero.

Question 13

A particle of mass $$m is $$released from rest at height $$h$$ and slides down a frictionless track into a vertical loop of radius $$R. $$What is the minimum value of $$h so $$that the particle completes the loop?

Accepted Answer

$$h = 2.5R$$

Question 14

Which of the following best describes the difference between conservative and non-conservative forces?

Accepted Answer

Conservative forces do not dissipate energy, non-conservative forces do.

Question 15

A block of mass $$m$$ slides down a rough incline of height $$h$$ and comes to rest after traveling a distance $$d on $$the rough surface. If the coefficient of kinetic friction is $$\mu_k$$, which equation correctly relates $$h$$, $$d$$, and $$\mu_k$$?

Accepted Answer

$$mgh = \mu_k m g d$$

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