Q: A 10 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the maximum horizontal force that can be applied to the box before it starts to move?

$$f_{s,\,max} = \mu_s N = 0.4 \times (10 \times 9.8) = 39.2\ \mathrm{N}$$

Q: A 5 kg object is suspended from a spring with a spring constant $$k = 200\ \mathrm{N/m}. $$How far does the spring stretch from its equilibrium position?

$$\Delta x = \frac{mg}{k} = \frac{5 \times 9.8}{200} = 0.245\ \mathrm{m}$$

Q: A 70 kg astronaut weighs 686 N on Earth. What would be her weight on a planet where $$g = 3.7\ \mathrm{m/s^2$}$$?

$$W = mg = 70 \times 3.7 = 259\ \mathrm{N}$$

Q: A 2 kg block is pulled across a horizontal surface at constant speed by a force of 10 N. What is the coefficient of kinetic friction between the block and the surface?

$$\mu_k = \frac{F}{N} = \frac{10}{2 \times 9.8} = 0.51$$

Q: A 0.5 kg ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the net force acting on the ball at its highest point?

$$F_{net} = mg = 0.5 \times 9.8 = 4.9\ \mathrm{N}$$\ (downward)

Q: A 3 kg block is at rest on a 30° incline. What is the magnitude of the normal force acting on the block?

$$N = mg \cos \theta = 3 \times 9.8 \times \cos 30^\circ = 25.5\ \mathrm{N}$$

Q: A 2 kg object is attached to a spring and oscillates horizontally on a frictionless surface. If the spring constant is $$k = 50\ \mathrm{N/m}$$ and the object is displaced 0.1 m from equilibrium, what is the magnitude of the restoring force?

$$F_{sp} = kx = 50 \times 0.1 = 5\ \mathrm{N}$$

Q: A 60 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

$$w_{app} = m(g + a) = 60 \times (9.8 + 2) = 708\ \mathrm{N}$$

Q: A 1.2 kg object falls through honey ($$\eta = 10\ \mathrm{Pa \cdot s}$$, $$\rho = 1400\ \mathrm{kg/m^3$}) $$and quickly reaches terminal speed. If the object is a sphere of radius $$0.05\ \mathrm{m}$$, what is the magnitude of the drag force at terminal speed?

$$D = mg = 1.2 \times 9.8 = 11.76\ \mathrm{N}$$

Question 1

A 10 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the maximum horizontal force that can be applied to the box before it starts to move?

Accepted Answer

$$f_{s,\,max} = \mu_s N = 0.4 	imes (10 	imes 9.8) = 39.2\ \mathrm{N}$$

Question 2

A 5 kg object is suspended from a spring with a spring constant $$k = 200\ \mathrm{N/m}. $$How far does the spring stretch from its equilibrium position?

Accepted Answer

$$\Delta x = \frac{mg}{k} = \frac{5 	imes 9.8}{200} = 0.245\ \mathrm{m}$$

Question 3

A 70 kg astronaut weighs 686 N on Earth. What would be her weight on a planet where $$g = 3.7\ \mathrm{m/s^2$}$$?

Accepted Answer

$$W = mg = 70 	imes 3.7 = 259\ \mathrm{N}$$

Question 4

A 2 kg block is pulled across a horizontal surface at constant speed by a force of 10 N. What is the coefficient of kinetic friction between the block and the surface?

Accepted Answer

$$\mu_k = \frac{F}{N} = \frac{10}{2 	imes 9.8} = 0.51$$

Question 5

A 0.5 kg ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the net force acting on the ball at its highest point?

Accepted Answer

$$F_{net} = mg = 0.5 	imes 9.8 = 4.9\ \mathrm{N}$$\ (downward)

Question 6

A 1.5 kg object is moving through air at a constant speed. The drag force acting on it is $$12\ \mathrm{N}. $$What is the net force on the object?

Accepted Answer

$$F_{net} = 0$$

Question 7

A 3 kg block is at rest on a 30° incline. What is the magnitude of the normal force acting on the block?

Accepted Answer

$$N = mg \cos 	heta = 3 	imes 9.8 	imes \cos 30^\circ = 25.5\ \mathrm{N}$$

Question 8

A 2 kg object is attached to a spring and oscillates horizontally on a frictionless surface. If the spring constant is $$k = 50\ \mathrm{N/m}$$ and the object is displaced 0.1 m from equilibrium, what is the magnitude of the restoring force?

Accepted Answer

$$F_{sp} = kx = 50 	imes 0.1 = 5\ \mathrm{N}$$

Question 9

A 60 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$w_{app} = m(g + a) = 60 	imes (9.8 + 2) = 708\ \mathrm{N}$$

Question 10

A 1 kg ball is dropped from rest and reaches terminal velocity in air. If the drag force at terminal velocity is $$9.8\ \mathrm{N}$$, what is the acceleration of the ball at terminal velocity?

Accepted Answer

$$a = 0\ \mathrm{m/s^2$}$$

Question 11

A 2 kg block is connected by a light string to a 4 kg block on a frictionless table. A force of $$18\ \mathrm{N} is $$applied to the 4 kg block. What is the acceleration of the system?

Accepted Answer

$$a = \frac{F}{m_{total}} = \frac{18}{2 + 4} = 3\ \mathrm{m/s^2$}$$

Question 12

A 1.2 kg object falls through honey ($$\eta = 10\ \mathrm{Pa \cdot s}$$, $$\rho = 1400\ \mathrm{kg/m^3$}) $$and quickly reaches terminal speed. If the object is a sphere of radius $$0.05\ \mathrm{m}$$, what is the magnitude of the drag force at terminal speed?

Accepted Answer

$$D = mg = 1.2 	imes 9.8 = 11.76\ \mathrm{N}$$

Question 13

Two objects, each of mass $$m$$, are separated by a distance $$r. $$What is the magnitude of the gravitational force between them?

Accepted Answer

$$F = \frac{G m^2$}{r^2$}$$

Question 14

A 10 kg box is pulled up a 20° incline at constant speed. The coefficient of kinetic friction is 0.15. What is the magnitude of the friction force?

Accepted Answer

$$f_k = \mu_k N = 0.15 	imes 10 	imes 9.8 	imes \cos 20^\circ = 13.8\ \mathrm{N}$$

Question 15

A mosquito collides head-on with a truck. According to Newton's third law, which statement is correct?

Accepted Answer

The mosquito exerts the same magnitude force on the truck as the truck exerts on the mosquito.

Question 16

A 0.2 kg leaf falls through air and quickly reaches terminal velocity. If the drag force is proportional to $$v^2$$, which equation best describes the drag force at high Reynolds number?

Accepted Answer

$$D = \frac{1}{2} C_D \rho A v^2$

Question 17

A 50 kg skier starts from rest at the top of a 30 m high frictionless slope. What is his speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 30} = 24.2\ \mathrm{m/s}$$

Question 18

A 10 kg box is pulled to the right with a force of 50 N on a rough surface. The box accelerates at $$2\ \mathrm{m/s^2$}. $$What is the net force acting on the box?

Accepted Answer

$$F_{net} = ma = 10 	imes 2 = 20\ \mathrm{N}$$

Question 19

A 2 kg block is at rest on a table. What is the normal force acting on the block?

Accepted Answer

$$N = mg = 2 	imes 9.8 = 19.6\ \mathrm{N}$$

Mechanics I: Force and Motion, Interacting Systems, and Applications in Life Sciences

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