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, which 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. Based on the model of friction, which of the following could explain their different outcomes if Anna did not slide but Maria did?

Accepted Answer

The coefficient of static friction between Anna's tires and the road was higher than between Maria's tires and the road.

Question 3

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

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

$2$

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 $2\,\mathrm{m/s^2}$. If your mass is $60\,\mathrm{kg}$, what does the scale read?

Accepted Answer

$72\,\mathrm{kg}$

Question 7

Suppose 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

$30^\circ$

Question 8

Suppose I drive at constant speed around a circular track with radius $100\,\mathrm{m}$. The coefficient of static friction between my tires and the ground is $1.1$. How fast can I drive before sliding off the track?

Accepted Answer

$21\,\mathrm{m/s}$

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 $1\,\mathrm{m/s}$ per second. Anna weighs $60\,\mathrm{kg}$ and Bob weighs $80\,\mathrm{kg}$. How fast does Anna move as a result of pushing Bob? (Assume no friction.)

Accepted Answer

$0.75\,\mathrm{m/s}$ 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 $1\,\mathrm{kg}$, and the string can have a maximum tension of $40\,\mathrm{N}$ before it breaks. What is the maximum (upward) acceleration of the elevator before the string breaks?

Accepted Answer

$1.5\,\mathrm{m/s^2}$

Question 11

A child sleds down a $20^\circ$ snow slope. The child and sled together weigh $25\,\mathrm{kg}$. What is the magnitude of the normal force that the snow exerts on the bottom of the sled?

Accepted Answer

$240\,\mathrm{N}$

Question 12

If you throw a projectile 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, $g = 9.8\,\mathrm{m/s^2}$, and the ground is flat.)

Accepted Answer

$55.6\,\mathrm{m}$

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 be too short

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

$	an^{-1}(0.4)$

Question 15

Suppose you apply a net force of $15\,\mathrm{N}$ to an object with a mass of $5\,\mathrm{kg}$. What is its acceleration?

Accepted Answer

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

Question 16

Suppose three blocks with masses $7\,\mathrm{kg}$, $3\,\mathrm{kg}$, and $5\,\mathrm{kg}$ are stacked on a table. The table is accelerating upward at $2\,\mathrm{m/s^2}$. What is the magnitude of the force of the table on the bottom block?

Accepted Answer

$98\,\mathrm{N}$

Question 17

Suppose the set-up in Question 25 was instead on the moon, where the acceleration due to gravity is $1.6\,\mathrm{m/s^2}$. What would be the magnitude of the force of the table on the bottom block?

Accepted Answer

$14.5\,\mathrm{N}$

Question 18

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

Accepted Answer

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

Question 19

Consider two vectors $\vec{A}$ and $\vec{B}$, both with non-zero magnitude and perpendicular to one another. Let $\vec{C}$ be the vector sum of $\vec{A}$ and $\vec{B}$. What is the magnitude of $\vec{C}$?

Accepted Answer

$C = \sqrt{A^2 + B^2}$

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

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