Q: A passenger on a Ferris wheel moves in a vertical circle of radius $$R$$ with constant speed $$v. $$What is the expression for the normal force $$N_{\text{top}}$$ exerted by the seat on the passenger at the top of the circle?

$$N_{\text{top}} = m(g - \frac{v^2$}{R})$$

Question 1

A car engine of weight $$w$$ hangs from a chain attached at point O to two other chains, as shown in the image. The chain to the ceiling makes a $$60^\circ$$ angle with the vertical. If the weights of the ring and chains are negligible, what is the expression for the tension $$T_3 in $$the chain attached to the ceiling in terms of $$w$$?

Accepted Answer

$$T_3$$ = \frac{w}{\cos 60^\circ}$$

Question 2

A 500-N crate is pulled across a level floor. The minimum force required to start moving the crate is 230 N, and the force required to keep it moving at constant velocity is 200 N. What is the coefficient of static friction $$\mu_s$$ between the crate and the floor?

Accepted Answer

$$\mu_s = 0.46$$

Question 3

A 25.0-kg sled is attached by a 5.00-m rope to a post and revolves uniformly in a circle on frictionless ice, making five complete revolutions every minute. What is the magnitude of the force $$F$$ exerted by the rope on the sled?

Accepted Answer

$$F = 34.2\ \mathrm{N}$$

Question 4

A 50.0-kg woman stands on a bathroom scale in an elevator that is slowing to a stop while moving downward. If the elevator and its load have a combined mass of 800 kg and decelerate uniformly from 10.0 m/s to rest over 25.0 m, what will the scale read during the deceleration?

Accepted Answer

$$\approx 590\ \mathrm{N}$$

Question 5

A toboggan loaded with students (total weight $$w) $$slides down a frictionless slope inclined at angle $$	heta. $$What is the acceleration $$a of $$the toboggan?

Accepted Answer

$$a = g \sin 	heta$$

Question 6

A block of ice with mass 8.00 kg slides down a 1.50-m-long frictionless ramp and reaches a speed of 2.50 m/s at the bottom. What is the angle $$	heta of $$the ramp with respect to the horizontal?

Accepted Answer

$$	heta = 12.2^\circ$$

Question 7

If the same block of ice in the previous question is opposed by a constant friction force of 10.0 N parallel to the ramp, what would be its speed at the bottom?

Accepted Answer

$$v = 1.22\ \mathrm{m/s}$$

Question 8

A human body (mass 50 kg) falls through air in a spread-eagle position. If the drag constant $$D = 0.25\ \mathrm{kg/m}$$, what is the terminal speed $$v_t$$?

Accepted Answer

$$v_t = 44.3\ \mathrm{m/s}$$

Question 9

Which of the following best describes the difference between static and kinetic friction?

Accepted Answer

Static friction acts when there is no relative motion between surfaces; kinetic friction acts when surfaces slide past each other.

Question 10

A box is pushed across a horizontal surface. Which of the following statements is true about the normal force acting on the box?

Accepted Answer

It is equal in magnitude and opposite in direction to the weight if the surface is horizontal and no other vertical forces act.

Question 11

A crate is at rest on a horizontal surface. A horizontal force is gradually increased until the crate just begins to move. Which force is responsible for keeping the crate at rest before it moves?

Accepted Answer

Static friction

Question 12

Which of the following materials has the lowest coefficient of kinetic friction according to the provided table?

Accepted Answer

Teflon on Teflon

Question 13

A loaded filing cabinet is easier to move using a cart with wheels than by sliding it. This is primarily because:

Accepted Answer

The coefficient of rolling friction is much less than the coefficient of sliding friction.

Question 14

A passenger on a Ferris wheel moves in a vertical circle of radius $$R$$ with constant speed $$v. $$What is the expression for the normal force $$N_{	ext{top}}$$ exerted by the seat on the passenger at the top of the circle?

Accepted Answer

$$N_{	ext{top}} = m(g - \frac{v^2$}{R})$$

Question 15

Which of the following is NOT a fundamental force of nature?

Accepted Answer

Frictional force

Question 16

A 200-kg iceboat is at rest on a frictionless surface. A wind blows along the direction of the runners, and after 4.0 s, the iceboat is moving at 6.0 m/s. What is the magnitude of the constant horizontal force exerted by the wind?

Accepted Answer

$$F = 300\ \mathrm{N}$$

Question 17

Suppose a constant horizontal friction force of 100 N opposes the motion of the iceboat in the previous question. What constant force must the wind exert to cause the same acceleration?

Accepted Answer

$$F = 400\ \mathrm{N}$$

Dynamics of Particles: Equilibrium, Friction, and Circular Motion

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