Q: A ladder of length $$L$$ and mass $$m$$ leans against a frictionless wall, making an angle $$\theta$$ with the floor. The coefficient of static friction between the ladder and the floor is $$\mu_s. $$What is the minimum value of $$\mu_s so $$the ladder does not slip?

$$\mu_s = \frac{1}{2} \cot \theta$$

Question 1

A particle is moving to the right with velocity $$\vec{v}$$ and experiences an acceleration $$\vec{a}$$ directed to the left. What will this acceleration do to the particle's motion?

Accepted Answer

It will slow down and curve downward.

Question 2

Which of the following vector diagrams correctly represents $$2\vec{A} - \vec{B} if$$ $$\vec{A}$$ points up and to the right, and $$\vec{B}$$ points up and to the left?

Accepted Answer

A vector pointing to the right.

Question 3

A position-versus-time graph shows a curve that starts at the origin and increases with a decreasing slope, approaching a horizontal line. Which velocity-versus-time graph matches this motion?

Accepted Answer

A line that starts positive and decreases toward zero.

Question 4

An elevator suspended by a cable is moving upward and slowing to a stop. Which free-body diagram is correct?

Accepted Answer

The upward tension force is less than the downward gravitational force, causing a net downward force.

Question 5

A 50-kg student ($$mg = 490\ \mathrm{N}) $$stands on a scale in a 1000-kg elevator at rest. As the elevator accelerates upward, the scale reads:

Accepted Answer

$$\u003e 490\ \mathrm{N}$$

Question 6

Boxes A and B are sliding to the right on a frictionless surface. Hand H is slowing them. Box A has a larger mass than B. Considering only the horizontal forces, which equation is correct?

Accepted Answer

$$F_{\mathrm{hand}} = F_{\mathrm{A\ on\ B}} + F_{\mathrm{B\ on\ A}} + F_{\mathrm{friction}}$$

Question 7

A particle with the potential energy shown in the graph is moving to the right. It has $$1.0\ \mathrm{J} of $$kinetic energy at $$x = 1.0\ \mathrm{m}. In $$the region $$1.0\ \mathrm{m} \u003c x \u003c 2.0\ \mathrm{m}$$, the particle is:

Accepted Answer

Slowing down.

Question 8

A roller coaster starts from rest at height $$h$$ and must complete a vertical loop of radius $$R$$ without losing contact at the top. What is the minimum height $$h$$ required for the coaster to safely complete the loop?

Accepted Answer

$$h = \frac{5}{2}R$$

Question 9

A wood block of mass $$M is at $$rest on a slope at angle $$	heta. A $$bullet of mass $$m$$ and initial speed $$v_0 is $$fired parallel to the slope and becomes embedded in the block. What is the final speed of the block and bullet immediately after the collision?

Accepted Answer

$$v_f = \frac{m v_0$}{M + m}$$

Question 10

Block A (mass $$m_A) $$rests on a table and is connected by a string over a pulley to block B (mass $$m_B) $$hanging off the edge. The coefficient of kinetic friction between block A and the table is $$\mu_k. $$Which equation gives the acceleration $$a of $$the system?

Accepted Answer

$$a = \frac{m_B g - \mu_k m_A g}{m_A + m_B}$$

Question 11

A ladder of length $$L$$ and mass $$m$$ leans against a frictionless wall, making an angle $$	heta$$ with the floor. The coefficient of static friction between the ladder and the floor is $$\mu_s. $$What is the minimum value of $$\mu_s so $$the ladder does not slip?

Accepted Answer

$$\mu_s = \frac{1}{2} \cot 	heta$$

Question 12

A car is moving at constant velocity on a straight road. Which of the following statements is true?

Accepted Answer

The net force on the car is zero.

Question 13

A ball is thrown straight up. At the highest point of its trajectory, which of the following is true?

Accepted Answer

The velocity is zero and the acceleration is downward.

Question 14

A block slides down a frictionless incline. Which energy transformation occurs?

Accepted Answer

Potential energy is converted to kinetic energy.

Question 15

A 2-kg object is acted on by a net force of $$6\ \mathrm{N}. $$What is its acceleration?

Accepted Answer

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

Question 16

A 5-kg box is pulled across a horizontal surface with a force of $$20\ \mathrm{N}. $$The coefficient of kinetic friction is $$0.2. $$What is the acceleration of the box?

Accepted Answer

$$1.2\ \mathrm{m/s^2$}$$

Question 17

A ball is whirled in a horizontal circle on a string. If the string breaks, what path does the ball follow?

Accepted Answer

It moves in a straight line tangent to the circle.

Question 18

A car rounds a flat curve of radius $$r at $$speed $$v. $$What is the minimum coefficient of friction $$\mu$$ required to prevent slipping?

Accepted Answer

$$\mu = \frac{v^2$}{g r}$$

Question 19

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

Accepted Answer

$$h = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Fundamental Concepts in Introductory Physics: Kinematics, Dynamics, and Energy

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