Q: A 10 kg block is pulled up a $$30^\circ$$ incline at constant speed by a force parallel to the incline. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the magnitude of the pulling force?

$$F = mg\sin\theta + \mu_k mg\cos\theta$$

Q: A 2 kg block is attached to a wall by a spring ($$k = 50\ \mathrm{N/m}) $$and rests on a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.1. If $$the block is pulled so the spring is stretched 0.2 m and then released, what is the net force on the block immediately after release?

$$F_{\text{net}} = -kx - \mu_k mg$$

Question 1

A 5 kg box rests on a horizontal surface. A horizontal force of 20 N is applied to the box, but it does not move. If the coefficient of static friction between the box and the surface is $$\mu_s = 0.5$$, what is the magnitude of the frictional force acting on the box?

Accepted Answer

$$20\ \mathrm{N}$$

Question 2

A car of mass $$m is $$moving at a constant speed $$v$$ around a flat, circular track of radius $$r. $$What is the minimum coefficient of static friction $$\mu_s$$ required to prevent the car from sliding off the track?

Accepted Answer

$$\mu_s = \dfrac{v^2$}{rg}$$

Question 3

A 2 kg object is attached to a spring with a spring constant $$k = 100\ \mathrm{N/m}. $$The spring is stretched 0.1 m from its equilibrium position and released from rest. What is the magnitude of the force exerted by the spring at this instant?

Accepted Answer

$$10\ \mathrm{N}$$

Question 4

A skydiver of mass $$80\ \mathrm{kg}$$ reaches terminal velocity during free fall. If the drag force is given by $$F_{	ext{drag}} = bv$$, where $$b = 60\ \mathrm{kg/s}$$, what is the terminal velocity $$v_t$$?

Accepted Answer

$$v_t = \dfrac{mg}{b}$$

Question 5

A 10 kg block is pulled up a $$30^\circ$$ incline at constant speed by a force parallel to the incline. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the magnitude of the pulling force?

Accepted Answer

$$F = mg\sin	heta + \mu_k mg\cos	heta$$

Question 6

Which of the following statements best describes Newton’s Third Law?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 7

A satellite orbits Earth in a circular orbit of radius $$r. $$According to Newton’s Law of Gravitation, what is the expression for the gravitational force acting on the satellite?

Accepted Answer

$$F = \dfrac{GMm}{r^2$}$$

Question 8

A 3 kg object is acted on by three forces: $$\vec{F}_1 = (4\ \mathrm{N})\hat{i}$$, $$\vec{F}_2 = (-2\ \mathrm{N})\hat{j}$$, and $$\vec{F}_3 = (3\ \mathrm{N})\hat{i} + (6\ \mathrm{N})\hat{j}. $$What is the magnitude of the object’s acceleration?

Accepted Answer

$$a = \dfrac{\sqrt{(4+3)^2$ + (-2+6)^2$}}{3}$$

Question 9

A 1.5 kg puck slides on a frictionless horizontal surface. A constant force of $$6\ \mathrm{N} is $$applied at an angle of $$60^\circ$$ above the horizontal. What is the horizontal acceleration of the puck?

Accepted Answer

$$a_x = \dfrac{6\cos 60^\circ}{1.5}$$

Question 10

A 2 kg block is attached to a wall by a spring ($$k = 50\ \mathrm{N/m}) $$and rests on a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.1. If $$the block is pulled so the spring is stretched 0.2 m and then released, what is the net force on the block immediately after release?

Accepted Answer

$$F_{	ext{net}} = -kx - \mu_k mg$$

Question 11

A 70 kg astronaut in space pushes on a 140 kg satellite with a force of 21 N. According to Newton’s Third Law, what is the magnitude of the force exerted by the satellite on the astronaut?

Accepted Answer

$$21\ \mathrm{N}$$

Question 12

A ball of mass $$m is $$whirled in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the required centripetal force?

Accepted Answer

$$F_c = \dfrac{mv^2$}{r}$$

Question 13

A 50 kg crate is at rest on a horizontal floor. The coefficient of static friction is $$\mu_s = 0.4. $$What is the minimum horizontal force required to start moving the crate?

Accepted Answer

$$F = \mu_s mg$$

Question 14

A 2 kg object moves in a circle of radius 3 m at a constant speed of 6 m/s. What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = m\dfrac{v^2$}{r}$$

Question 15

A 1 kg ball is dropped from rest from a height. As it falls, air resistance is proportional to its velocity: $$F_{	ext{drag}} = bv. $$Which of the following best describes the motion as it approaches terminal velocity?

Accepted Answer

The net force on the ball approaches zero.

Question 16

A 4 kg object is acted on by two forces: $$\vec{F}_1 = (8\ \mathrm{N})\hat{i}$$ and $$\vec{F}_2 = (6\ \mathrm{N})\hat{j}. $$What is the magnitude of the acceleration?

Accepted Answer

$$a = \dfrac{\sqrt{8^2$ + 6^2$}}{4}$$

Question 17

A 10 kg box is suspended by a vertical rope. What is the tension in the rope if the box is at rest?

Accepted Answer

$$T = mg$$

Question 18

A 5 kg block is pushed across a horizontal surface with a force of 30 N. The coefficient of kinetic friction is $$\mu_k = 0.3. $$What is the acceleration of the block?

Accepted Answer

$$a = \dfrac{30 - \mu_k mg}{5}$$

Question 19

A 2 kg mass is attached to a spring and oscillates horizontally on a frictionless surface. If the spring constant is $$k = 80\ \mathrm{N/m}$$, what is the period of oscillation?

Accepted Answer

$$T = 2\pi\sqrt{\dfrac{m}{k}}$$

Forces and Translational Dynamics: Study Guide for PHYS 210 Exam 2

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