Q: A hiker pulls a friend up a hill inclined at $$30^\circ to $$the horizontal. If the coefficient of static friction between the hiker’s boots and the hill is $$0.80$$ and his mass is $$65 kg$$, what is the maximum force he can exert parallel to the hill without slipping? (Take $$g = 9.8 m/s$^2)$$

$$F_{max} = \mu_s (m g \cos \theta)$$

Question 1

A ball is dropped from a pole attached to a cart moving at constant velocity. In the Earth’s reference frame, what is the shape of the ball’s trajectory?

Accepted Answer

A parabola

Question 2

Which of the following statements about vector addition and subtraction is correct?

Accepted Answer

Vector addition is commutative, but vector subtraction is not.

Question 3

A ball is thrown at an angle $$	heta$$ above the horizontal with initial speed $$v_i. $$What is the horizontal component of its velocity?

Accepted Answer

$$v_i \cos 	heta$$

Question 4

A crate is at rest on a horizontal floor. You push it gently at first, then with increasing force, but it does not move. What happens to the force of static friction as you increase your push?

Accepted Answer

It increases in magnitude.

Question 5

A baseball player hits a fly ball with an initial horizontal velocity of 30 m/s and a vertical velocity of 40 m/s. What is the speed of the ball at the highest point of its flight?

Accepted Answer

30 m/s

Question 6

Which of the following best describes the work done by the normal force on an object sliding across a horizontal surface?

Accepted Answer

It is zero.

Question 7

A hiker pulls a friend up a hill inclined at $$30^\circ to $$the horizontal. If the coefficient of static friction between the hiker’s boots and the hill is $$0.80$$ and his mass is $$65 kg$$, what is the maximum force he can exert parallel to the hill without slipping? (Take $$g = 9.8 m/s$^2)$$

Accepted Answer

$$F_{max} = \mu_s (m g \cos 	heta)$$

Question 8

Which of the following is true about the force of kinetic friction?

Accepted Answer

It is proportional to the normal force and independent of the contact area.

Question 9

A block slides down a frictionless incline of height $$h. $$What is the work done by gravity?

Accepted Answer

$$W = mgh$$

Question 10

Under what condition is the scalar (dot) product of two vectors zero?

Accepted Answer

When the vectors are perpendicular

Question 11

A suitcase is on a conveyor belt inclined at $$20^\circ. If $$the maximum acceleration before slipping is $$4.0 m/s$^2$$, what is the coefficient of static friction $$\mu_s$$?

Accepted Answer

$$\mu_s = (g \sin 20^\circ + 4.0) / (g \cos 20^\circ)$$

Question 12

Which of the following is a correct statement about projectile motion near Earth’s surface (neglecting air resistance)?

Accepted Answer

The horizontal velocity remains constant.

Question 13

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 14

In polar coordinates, can the radial coordinate $$r be $$negative?

Accepted Answer

No

Question 15

A block of mass $$m is $$pulled up a rough incline at constant speed. The coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the frictional force?

Accepted Answer

$$\mu_k m g \cos 	heta$$

Question 16

A car of mass $$m_1$$ moving at velocity $$\vec{v}_{1i}$$ collides with a stationary car of mass $$m_2. $$After the collision, both cars move off at angles to the original direction. Which principle allows you to solve for their final velocities?

Accepted Answer

Conservation of momentum in two dimensions

Question 17

Which of the following best describes the effect of the component of acceleration perpendicular to the instantaneous velocity in two-dimensional motion?

Accepted Answer

It changes the direction of the velocity but not its magnitude.

Question 18

A block slides down an incline of angle $$	heta$$ and height $$h. $$What is the displacement along the incline?

Accepted Answer

$$h / \sin 	heta$$

Question 19

Which of the following is true about the work done by gravity on an object descending a vertical distance $$h$$?

Accepted Answer

It is independent of the path and equals $$mgh.$$

Chapter 10: Motion in a Plane – Physics Study Guide

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