Question 1

A projectile is shot from ground level at an angle $	heta$ above the horizontal. Assuming the ground is flat and air resistance is negligible, what value of $	heta$ maximizes the horizontal distance traveled by the projectile before it hits the ground?

Accepted Answer

$45^\circ$

Question 2

Maria drives around a curve in the road and slides off the side of the road. Anna drives around the same curve and stays on the road. Based on the model of friction, which of the following could explain their different outcomes?

Accepted Answer

Anna drove more slowly around the curve.

Question 3

Suppose you travel 1 mile north, then one mile northeast, then one mile southeast. How far are you from your starting point?

Accepted Answer

$\sqrt{2}$ miles

Question 4

Suppose projectile 1 is shot straight up, and projectile 2 is shot at a $30^\circ$ angle with respect to the horizontal at the same speed. What is the ratio of the maximum height achieved by projectile 1 to that achieved by projectile 2?

Accepted Answer

$\frac{1}{\sin^2 30^\circ}$

Question 5

Suppose two people pull with a force of 100 newtons on opposite sides of a rope. What is the tension in the rope?

Accepted Answer

100 newtons

Question 6

You are standing on a scale in an elevator that is accelerating upward at a rate of $2\ \mathrm{m/s^2}$. If your mass is $60\ \mathrm{kg}$, what does the scale read?

Accepted Answer

72 kilograms

Question 7

An object is sliding down a frictionless ramp. The acceleration of the object is measured to be $4\ \mathrm{m/s^2}$. What is the angle of the ramp?

Accepted Answer

$\arcsin(0.4)$

Question 8

Suppose you drive at constant speed around a circular track with radius 100 meters. The coefficient of static friction between your tires and the ground is 1.1. How fast can you drive before sliding off the track?

Accepted Answer

$v = \sqrt{\mu_s g r}$

Question 9

Anna and Bob are standing still on ice skates. Anna pushes Bob as hard as she can, and as a result he starts moving at 1 meter per second. Anna weighs 60 kilograms and Bob weighs 80 kilograms. How fast does Anna move as a result of pushing Bob? (Assume no friction.)

Accepted Answer

0.75 meters per second

Question 10

Suppose three beads are connected by pieces of string, hanging from the ceiling of an elevator as shown. Each bead has a mass of 1 kilogram, and the string can have a maximum tension of 40 newtons before it breaks. What is the maximum (upwards) acceleration of the elevator before the string breaks?

Accepted Answer

$2.5\ \mathrm{m/s^2}$

Question 11

A child slides down a 20 degree snow slope. The child and sled together weigh 25 kilograms. What is the magnitude of the normal force that the snow exerts on the bottom of the sled?

Accepted Answer

$25g \cos 20^\circ$

Question 12

If a projectile is fired at $25\ \mathrm{m/s}$ at an angle of $30^\circ$ above the ground, how far does it go before it lands? (Assume no air resistance, $g = 10\ \mathrm{m/s^2}$, and the ground is flat.)

Accepted Answer

$61.1$ meters

Question 13

Suppose you did not take into account the initial height of the object when calculating projectile range. How would your answer to question 14 change?

Accepted Answer

It would underestimate the range

Question 14

Suppose the coefficient of static friction between an object and the table is 0.4. To what angle can I tilt the table without the object sliding?

Accepted Answer

$\arctan(0.4)$

Question 15

Suppose instead of throwing a ball vertically, you throw it horizontally from a height of 1.5 meters above the ground at the same speed. How much further would the one on the moon travel before it hit the ground, compared to Earth? (Assume $g_{moon} = 1.6\ \mathrm{m/s^2}$, $g_{earth} = 9.8\ \mathrm{m/s^2}$.)

Accepted Answer

2.45 times further

Question 16

Which of the following is true of acceleration and velocity vectors of an object undergoing uniform circular motion?

Accepted Answer

They are perpendicular

Question 17

Suppose a bird has a mid-air collision with a bee. Which of the following is true?

Accepted Answer

The force the bird exerts on the bee is equal in magnitude to the force the bee exerts on the bird.

Question 18

Suppose you apply a net force of 15 newtons to an object with a mass of 5 kilograms. What is its acceleration?

Accepted Answer

$3\ \mathrm{m/s^2}$

Question 19

Consider two vectors $\vec{A}$ and $\vec{B}$. Let $\vec{C}$ be the vector sum of $\vec{A}$ and $\vec{B}$. Let $|A|$ be the magnitude of $\vec{A}$, $|B|$ the magnitude of $\vec{B}$, and $|C|$ the magnitude of $\vec{C}$. Which of the following is true?

Accepted Answer

$|C| \leq |A| + |B|$

Fundamental Concepts in Introductory Physics: Mechanics, Forces, and Motion

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