Q: Given the force of kinetic friction $$f_k = \mu_k N$$, and the skier's weight $$w = mg$$, what is the correct expression for the net force in the $$x-$$direction?

$$F_{\text{net},x} = w_x - f_k$$

Q: A spring with $$k = 500\ \text{N/m} is $$stretched by $$0.02\ \text{m}. $$What is the magnitude of the force exerted by the spring?

$$F = 500 \times 0.02 = 10\ \text{N}$$

Q: Which of the following correctly gives the $$x$$ and $$y$$ components of the skier's weight on the incline?

$$w_x = w\sin \theta;\ w_y = w\cos \theta$$

Q: A skier of mass $$60\ \text{kg}$$ slides down a $$25^\circ$$ slope with $$\mu_k = 0.10. $$What is the skier's acceleration down the slope? ($$g = 9.8\ \text{m/s}^2)$$

$$a = 9.8(\sin 25^\circ - 0.10 \cos 25^\circ) \approx 3.1\ \text{m/s}^2$$

Q: If the force required to stretch a spring by $$0.05\ \text{m} is$$ $$10\ \text{N}$$, what is the spring constant $$k$$?

$$k = \dfrac{10}{0.05} = 200\ \text{N/m}$$

Question 1

A skier of mass $$m$$ starts from rest and slides down a snowy slope inclined at $$25^\circ to $$the horizontal. The coefficient of kinetic friction between the skis and the snow is $$\mu_k. $$Which of the following correctly expresses the skier's acceleration down the slope?

Accepted Answer

$$a_x = \dfrac{mg\sin 25^\circ - \mu_k mg\cos 25^\circ}{m}$$

Question 2

In the context of the skier on the incline, what is the correct expression for the normal force $$N$$ acting on the skier?

Accepted Answer

$$N = mg\cos 25^\circ$$

Question 3

A tug-of-war team pulls on a rope with a total force of $$F. If $$the ground is muddy and the coefficient of static friction between their shoes and the ground is $$\mu_s$$, what is the maximum force the team can exert without slipping, assuming their total mass is $$M$$?

Accepted Answer

$$F_{	ext{max}} = \mu_s M g$$

Question 4

Which of the following best describes the net force in the $$y-$$direction for the skier on the incline?

Accepted Answer

$$F_{	ext{net},y} = N - w_y$$

Question 5

For the skier on the incline, which component of acceleration is zero?

Accepted Answer

$$a_y$$

Question 6

Given the force of kinetic friction $$f_k = \mu_k N$$, and the skier's weight $$w = mg$$, what is the correct expression for the net force in the $$x-$$direction?

Accepted Answer

$$F_{	ext{net},x} = w_x - f_k$$

Question 7

A spring has a spring constant $$k = 100\ 	ext{N/m}. $$According to Hooke's Law, what is the force required to stretch the spring by a displacement $$x$$?

Accepted Answer

$$F = 100x$$

Question 8

A spring with $$k = 500\ 	ext{N/m} is $$stretched by $$0.02\ 	ext{m}. $$What is the magnitude of the force exerted by the spring?

Accepted Answer

$$F = 500 	imes 0.02 = 10\ 	ext{N}$$

Question 9

Which of the following correctly gives the $$x$$ and $$y$$ components of the skier's weight on the incline?

Accepted Answer

$$w_x = w\sin 	heta;\ w_y = w\cos 	heta$$

Question 10

A skier of mass $$60\ 	ext{kg}$$ slides down a $$25^\circ$$ slope with $$\mu_k = 0.10. $$What is the skier's acceleration down the slope? ($$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$a = 9.8(\sin 25^\circ - 0.10 \cos 25^\circ) \approx 3.1\ 	ext{m/s}^2$$

Question 11

In a tug-of-war, if both teams pull with equal force and the rope does not move, what can be said about the net force on the rope?

Accepted Answer

The net force on the rope is zero.

Question 12

A block of mass $$m is at $$rest on an incline of angle $$	heta. $$What is the minimum coefficient of static friction $$\mu_s$$ required to keep the block from sliding down?

Accepted Answer

$$\mu_s = 	an 	heta$$

Question 13

A skier starts from rest and travels a distance $$d$$ down a $$25^\circ$$ slope with acceleration $$a. $$What is the time $$t$$ taken to reach the bottom?

Accepted Answer

$$t = \sqrt{\dfrac{2d}{a}}$$

Question 14

If the force required to stretch a spring by $$0.05\ 	ext{m} is$$ $$10\ 	ext{N}$$, what is the spring constant $$k$$?

Accepted Answer

$$k = \dfrac{10}{0.05} = 200\ 	ext{N/m}$$

Question 15

A skier of mass $$m is $$sliding down a frictionless $$25^\circ$$ slope. What is the normal force acting on the skier?

Accepted Answer

$$N = mg\cos 25^\circ$$

Question 16

A block is pulled up a rough incline at constant speed. Which of the following statements is true about the forces acting parallel to the incline?

Accepted Answer

The pulling force equals the sum of friction and the component of gravity down the incline.

Force and Newton's Laws: Applications and Problem Solving

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