Q: A 10 kg box slides down a frictionless incline from height $$h_i = 2.0 m$$, then crosses a rough horizontal surface ($$\mu_k = 0.25$$, $$d = 1.0 m) $$before rising up a frictionless circular arc. What is the final height $$h_f$$ where the box comes to rest?

$$h_f = h_i - (\mu_k d) = 2.0 - (0.25 \times 1.0) = 1.75 m$

Question 1

A 5 kg cat climbs from the base to the restaurant of the CN Tower, 350 m above the ground. Using the general equation for gravitational potential energy, what is the change in the cat's gravitational potential energy? (Assume $$r_1 = 6$$,371,000$$ m and r_2$ = 6,371,350 m$$, $$m_E = 5.97 	imes 10$$^{24}$$ kg, G = 6.67$$ 	imes $$10^{-11} N$$·m$$^2/kg$^2.)$$

Accepted Answer

$$\Delta U_g = -Gm_Em \left( \frac{1}{r_2$} - \frac{1}{r_1$} \right) \approx 1,640 J$$

Question 2

Which of the following statements about escape speed from Earth is correct?

Accepted Answer

Escape speed is given by $$v_{escape} = \sqrt{2Gm_E/r_E}$$ and is independent of the object's mass.

Question 3

A satellite is launched from Earth's surface. At what point is its gravitational potential energy zero, according to the general model?

Accepted Answer

At infinite distance from Earth.

Question 4

A uniform ladder leans against a frictionless wall, making an angle with the ground. Which force provides the torque that prevents the ladder from slipping?

Accepted Answer

The static friction force from the floor.

Question 5

A wrench of length $$l is $$used to loosen a bolt. If a force $$F is $$applied perpendicular to the wrench at its end, what is the torque produced?

Accepted Answer

$$	au = Fl$$

Question 6

Two masses, $$m_1$$ and $$m_2$$, are separated by a distance $$r. $$What is the gravitational force between them?

Accepted Answer

$$F = Gm_1m_2/r^2$

Question 7

A uniform meter stick is supported at both ends by scales, each reading 0.5 N. If a 5.0 kg brick is placed 40 cm from the left end, what happens to the readings on the scales?

Accepted Answer

The left scale reads more than 0.5 N, the right less.

Question 8

A sports car accelerates from 0 to 30 mph in 1.5 s. Assuming constant power and neglecting air resistance, how long does it take to reach 60 mph from rest?

Accepted Answer

4.5 s

Question 9

Which of the following best describes a rigid body?

Accepted Answer

A body with constant interparticle distances and fixed shape.

Question 10

A 10 kg box slides down a frictionless incline from height $$h_i = 2.0 m$$, then crosses a rough horizontal surface ($$\mu_k = 0.25$$, $$d = 1.0 m) $$before rising up a frictionless circular arc. What is the final height $$h_f$$ where the box comes to rest?

Accepted Answer

$$h_f = h_i - (\mu_k d) = 2.0 - (0.25 	imes 1.0) = 1.75 m$

Question 11

Which of the following forces produces the greatest torque on a door about its hinge?

Accepted Answer

A force applied perpendicular to the door at the edge farthest from the hinge.

Question 12

A uniform beam is balanced at its center. If a mass $$m is $$hung at a distance $$d to $$the left and a mass $$2m is $$hung to the right, at what distance from the center must $$2m be $$hung for equilibrium?

Accepted Answer

$$d/2$$

Question 13

The center of mass of a system of particles is given by which of the following equations?

Accepted Answer

$$x_{cm} = \frac{1}{M} \sum_i m_i x_i$$

Question 14

A ladder leans against a wall. If the axis of rotation is chosen at the bottom of the ladder, what is the sign of the torque produced by the normal force from the wall?

Accepted Answer

Positive

Question 15

A gymnast balances on one hand. What must be true about the torques acting on her body?

Accepted Answer

The net torque about her center of mass is zero.

Question 16

A force $$F is $$applied at an angle $$	heta to a $$lever arm $$l. $$What is the general formula for the torque produced?

Accepted Answer

$$	au = Fl \sin 	heta$$

Question 17

A 3.0 kg object is made of three uniform bars, each 1.0 kg and 4.0 m long, arranged in an L-shape in the x-y plane. What are the coordinates of the center of mass?

Accepted Answer

(2.0 m, 2.0 m)

Question 18

Which of the following is a condition for static equilibrium?

Accepted Answer

The sum of all forces and the sum of all torques on the object must be zero.

Extended Bodies at Rest: Gravitational Potential Energy, Rigid Bodies, Torque, and Equilibrium

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