Q: A skydiver reaches terminal velocity during free fall. Which equation best describes the terminal speed if the drag force is proportional to the square of the velocity?

$$v_{\text{terminal}} = \sqrt{\frac{mg}{D}}$$

Q: A block is sliding on a surface and the friction force is proportional to the velocity. What is the terminal speed if the resistance force is $$F_{\text{resistance}} = -kv$$?

$$v_{\text{terminal}} = \frac{mg}{k}$$

Q: A block of mass $$m$$ moves in uniform circular motion of radius $$R$$ and speed $$v. $$What is the net force acting on the block?

$$F_{\text{net}} = m \frac{v^2$}{R}$$

Question 1

A skydiver reaches terminal velocity during free fall. Which equation best describes the terminal speed if the drag force is proportional to the square of the velocity?

Accepted Answer

$$v_{	ext{terminal}} = \sqrt{\frac{mg}{D}}$$

Question 2

An engine of weight $$w is $$suspended by three chains as shown. If chain $$T_3$$ makes a $$60^\circ$$ angle with the horizontal, what is the tension in $$T_3$$?

Accepted Answer

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

Question 3

A car of weight $$w is at $$rest on a ramp inclined at angle $$\alpha. $$What is the magnitude of the normal force acting on the car?

Accepted Answer

$$n = w \cos \alpha$$

Question 4

A cart of weight $$w_1 is $$attached to a bucket of weight $$w_2$$ via a frictionless pulley. The ramp is frictionless and inclined at $$15^\circ. $$When released, the cart accelerates up the ramp and the bucket accelerates downward. How does the cable tension $$T$$ compare to $$w_2$$?

Accepted Answer

$$T \u003c w_2$

Question 5

A traffic light weighing $$122\,	ext{N}$$ hangs from a cable tied to two other cables at $$37^\circ$$ and $$53^\circ to $$the horizontal. If the maximum tension in either upper cable is $$100\,	ext{N}$$, will the traffic light remain hanging?

Accepted Answer

No, the cable at $$37^\circ$$ will break.

Question 6

An iceboat and rider (total mass $$200\,	ext{kg}) $$accelerate from rest to $$6.0\,	ext{m/s} in$$ $$4.0\,	ext{s} on $$frictionless ice. What is the constant horizontal force exerted by the wind?

Accepted Answer

$$F_w = 300\,	ext{N}$$

Question 7

If a friction force of $$100\,	ext{N}$$ opposes the iceboat’s motion, what wind force is needed to achieve the same acceleration ($$a = 1.5\,	ext{m/s}^2$$)?

Accepted Answer

$$F_w = 400\,	ext{N}$$

Question 8

A woman of mass $$50\,	ext{kg}$$ stands on a scale in an elevator accelerating upward at $$2.0\,	ext{m/s}^2. $$What does the scale read?

Accepted Answer

$$590\,	ext{N}$$

Question 9

A toboggan slides down a hill of angle $$\alpha at $$constant speed. Which statement about the normal force $$n is $$correct?

Accepted Answer

$$n \u003c w$$

Question 10

You push a $$1.00\,	ext{kg}$$ tray with a $$0.50\,	ext{kg}$$ carton using a $$9.0\,	ext{N}$$ force on a frictionless surface. What is the acceleration of the system?

Accepted Answer

$$a_x = 6.0\,	ext{m/s}^2$$

Question 11

A block slides on a surface with kinetic friction. Which equation describes the kinetic friction force?

Accepted Answer

$$f_k = \mu_k n$$

Question 12

A person on a Ferris wheel moves in a vertical circle. What is the direction of the net force on the person?

Accepted Answer

Toward the center

Question 13

A falling apple is acted upon by which force(s) according to a correct free-body diagram?

Accepted Answer

Only gravity

Question 14

A block slides down a ramp at constant speed. What is the relationship between the friction force $$f$$ and the component of weight parallel to the ramp $$w \sin \alpha$$?

Accepted Answer

$$f = w \sin \alpha$$

Question 15

A block of mass $$m$$ slides on a surface with static friction. Which statement is true about the static friction force $$f_s$$?

Accepted Answer

$$f_s$$ can vary up to $$\mu_s n$$

Question 16

A block is sliding on a surface and the friction force is proportional to the velocity. What is the terminal speed if the resistance force is $$F_{	ext{resistance}} = -kv$$?

Accepted Answer

$$v_{	ext{terminal}} = \frac{mg}{k}$$

Question 17

A block of mass $$m$$ moves in uniform circular motion of radius $$R$$ and speed $$v. $$What is the net force acting on the block?

Accepted Answer

$$F_{	ext{net}} = m \frac{v^2$}{R}$$

Question 18

A block is sliding down a ramp and reaches constant speed. Which force is responsible for this behavior?

Accepted Answer

Friction force

Question 19

A block of mass $$m is $$suspended in an elevator accelerating downward at $$a_y. $$What is the tension in the cable?

Accepted Answer

$$T = m(g - a_y)$$

Applying Newton’s Laws: Statics, Dynamics, Friction, and Circular Motion

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