AP Physics Mechanics Exam Review: Test Booklet and Study Guide Key

Comprehensive 60-flashcard question-and-answer study set covering AP Physics Mechanics multiple-choice test booklet keys and study guide problems, including kinematics, Newton's laws, circular motion, gravitation, and center of mass.

In Period 6 Test Booklet Question 1, a student moves in the $+x$ direction with displacement $\Delta x_1$, then in the opposite direction with displacement $\Delta x_2$. What is the correct relationship between the magnitudes of the displacements?

(B) $|\Delta x_{\text{net}}| < |\Delta x_2| < |\Delta x_1|$

In Period 6 Test Booklet Question 2, what is the ratio of average acceleration for Carts A and B on the tracks?

(A) $1:2$

In Period 6 Test Booklet Question 3, what is the displacement after $2\,\text{s}$ if the acceleration graph is constant at $-5\,\text{m/s}^2$?

(B) $-10\,\text{m}$

In Period 6 Test Booklet Question 4, a ball released from the 20th floor falls 1 floor after $1\,\text{s}$. How many floors does it fall in $3\,\text{s}$?

(C) 7 to 10 floors

In Period 6 Test Booklet Question 5, what is the displacement of an object whose velocity-time graph drops linearly from $+4\,\text{m/s}$ to $-4\,\text{m/s}$ in $8\,\text{s}$?

(A) $0\,\text{m}$

In Period 6 Test Booklet Question 6, if Car A travels at $30\,\text{m/s}$ to the right and Car B travels at $10\,\text{m/s}$ to the right, what is the velocity of Car B relative to Car A?

(B) $-20\,\text{m/s}$

In Period 6 Test Booklet Question 7, a student stands on a raft of equal mass and walks to the opposite end. What describes their final position?

(C) Diagram showing raft moved backward and student at initial position relative to water

In Period 6 Test Booklet Question 8, three blocks are pushed along a rough surface. What forces are shown on the correct free-body diagram for Block 3?

(C) Diagram with $F_C$ right, $F_f$ left, $F_N$ up, and $F_G$ down

In Period 6 Test Booklet Question 9, what is the correct answer regarding the net force on an upward-traveling dart that strikes a vertically falling potato?

(B)

In Period 6 Test Booklet Question 10, how does the force exerted by a child's hand on a box compare to the force exerted by the box on the hand while raising the box with increasing speed?

(B) $F_{\text{hand on box}} = F_{\text{box on hand}}$, where $F_{\text{hand on box}}$ is larger as the box is being raised than when it was being held

In Period 6 Test Booklet Question 11, what does the acceleration versus net force graph show for a cart connected to a hanging mass via a pulley?

(A) Graph showing a straight line passing through the origin with a positive slope

In Period 6 Test Booklet Question 12, Block 1 slides toward a spring attached to Block 2. What do the acceleration of Block 2 and center-of-mass acceleration graphs show?

(A) Graph showing Acceleration of Block 2 rising/falling while Center-of-Mass Acceleration remains constant

In Period 6 Test Booklet Question 13, what are the magnitude and direction of acceleration for a meteoroid in a circular orbit $600\,\text{km}$ above a planet?

(C) $10\,\text{m/s}^2$ toward the center of the planet

In Period 6 Test Booklet Question 14, a spring with relaxed length $L_0$ is stretched by $\Delta x$ when attached to mass $m$. What is its length when attached to mass $4m$?

(D) $L_0 + 4\Delta x$

In Period 6 Test Booklet Question 15, what does the force versus radius graph show for a block on a string in a horizontal circle at constant speed?

(D) Graph showing force decreasing as radius increases ($F \propto \frac{1}{r}$)

In Period 6 Test Booklet Question 16, what force is exerted by the track on a $100\,\text{kg}$ cart at the top of a vertical loop where $r = 3\,\text{m}$ and $v = 6\,\text{m/s}$?

(A) $200\,\text{N}$

In Period 6 Test Booklet Question 17, if an automobile has a stopping distance $x$ at speed $v$, what is its stopping distance at speed $2v$?

(E) $4x$

In Period 6 Test Booklet Question 18, an object moves west at constant speed while acted on by forces of $10\,\text{N}$ north and $10\,\text{N}$ west. What are the magnitude and direction of the third force?

(D) $10\sqrt{2}\,\text{N}$, directed southeast

In Period 6 Test Booklet Question 19, Block A (mass $m$, $+v$) collides with Block B (mass $2m$, $-v$). What is the net force on Block B?

(D) $F$, because the net force is equal to the mutual contact force between the blocks

In Period 6 Test Booklet Question 20, a box of mass $m$ is suspended by two strings at $90^\circ$. What are the components of tension in string 2?

(A) Horizontal Component: $T_1 \cos(\theta_1)$; Vertical Component: $mg - T_1 \sin(\theta_1)$

In Period 3 Study Guide Question 1, can an astronaut at rest in deep space propel herself toward a space station by repeatedly moving her feet in opposite directions to each other?

No. Internal forces within a system (such as moving her feet relative to one another) cannot change the center-of-mass velocity of the system.

In Period 3 Study Guide Question 1, what is required for an astronaut at rest in deep space to change her center-of-mass position and return to the space station?

Without an external force or throwing mass away from herself, her overall center of mass will remain at rest relative to the space station.

In Period 3 Study Guide Question 2, where will a spacecraft of mass $3M$ and an object of mass $M$ meet when connected by a cable and pulled together in deep space with engines off?

They will meet at the center of mass of the system, which is located closer to the spacecraft (mass $3M$) at a distance of $\frac{1}{4}$ of the total separation distance away from the original position of the spacecraft.

In Period 3 Study Guide Question 3, what is the correct comparison of speeds $v_1, v_2,$ and $v_3$ for objects with velocities $v$, $-\frac{v}{3}$, and $-2v$?

$v_2 < v_1 < v_3$ (Speed is the absolute magnitude of velocity: $|-\frac{v}{3}| = \frac{v}{3}$, $|v| = v$, and $|-2v| = 2v$).

In Period 3 Study Guide Question 4, what are the respective directions and roles of centripetal acceleration and tangential acceleration for an orbiting body?

The centripetal acceleration is directed toward the center of the orbital body, while the tangential acceleration acts along the path of motion to change the object's speed.

In Period 3 Study Guide Question 5, why does placing a third identical book on top of two stacked books increase the normal force exerted by the bottom book on the middle book?

The normal force exerted by the bottom book on the middle book must support the weight of all books above it. Adding a third book increases the downward gravitational force that the middle book must support.

In Period 3 Study Guide Question 7, how is the force due to gravity exerted on a $10\,\text{kg}$ object determined from its speed-time graph?

Calculate acceleration $g$ from the slope of the speed-time graph (change in $v$ / change in $t$) and multiply by $10\,\text{kg}$ ($F_g = m \times g$).

In Period 3 Study Guide Question 8, what describes the force on a block and its motion immediately after being released from a compressed horizontal spring on a frictionless surface?

The spring exerts its maximum force, causing the block to experience its maximum acceleration and speed up immediately after release.

In Period 3 Study Guide Question 9, what are the magnitude and direction of the forces on the free-body diagram for a $4\,\text{kg}$ block pulled along a frictionless surface by a spring scale reading $10\,\text{N}$?

A diagram showing a horizontal pulling force $F = 10\,\text{N}$ to the right, a downward gravitational force $F_g = mg = 39.2\,\text{N}$, and an upward normal force $F_N = 39.2\,\text{N}$.

In Period 3 Study Guide Question 10, a car is at $x = 0$ from $t = 0$ to $1\,\text{s}$, at $x = 40\,\text{m}$ at $t = 5\,\text{s}$, and at $x = 80\,\text{m}$ at $t = 10\,\text{s}$. Is the average velocity from $t = 0$ to $5\,\text{s}$ less than from $t = 5$ to $10\,\text{s}$?

No, they are equal: Average velocity ($0-5\,\text{s}$) = $\frac{40\,\text{m} - 0\,\text{m}}{5\,\text{s} - 0\,\text{s}} = 8\,\text{m/s}$, and Average velocity ($5-10\,\text{s}$) = $\frac{80\,\text{m} - 40\,\text{m}}{10\,\text{s} - 5\,\text{s}} = 8\,\text{m/s}$.

In Period 3 Study Guide Question 11, two identical blocks sliding at $v_0$ stop in distances $d_1$ and $d_2$ in times $t_1$ and $t_2$. What represents the ratio $t_1 : t_2$?

$t_1 : t_2 = d_1 : d_2$ (Since average velocity is identical in both scenarios $v_{\text{avg}} = \frac{v_0}{2}$, time is directly proportional to stopping distance $d = v_{\text{avg}} \times t$).

In Period 3 Study Guide Question 12, what is the net upward force on a connected two-block system ($5\,\text{kg}$ upper, $10\,\text{kg}$ lower) when an upward force $F = 300\,\text{N}$ is applied?

$$F_{\text{net}} = 300\,\text{N} - (5\,\text{kg} + 10\,\text{kg})(10\,\text{m/s}^2) = 150\,\text{N}$$

In Period 3 Study Guide Question 12, what is the acceleration of the two-block system ($5\,\text{kg}$ and $10\,\text{kg}$) when pulled upward with a force of $300\,\text{N}$?

$10\,\text{m/s}^2$ upward ($a = \frac{150\,\text{N}}{15\,\text{kg}} = 10\,\text{m/s}^2$).

In Period 3 Study Guide Question 13, what is the acceleration of a student-bicycle system traveling in a circle at constant speed and constant radius?

$a = \frac{F_{\text{net}}}{m}$, directed toward the center of the circular path (where $F_{\text{net}}$ is the net centripetal force).

In Period 3 Study Guide Question 14, how is the acceleration due to gravity on another planet determined from a ball's height-versus-time graph in free fall from rest?

$g = \frac{2\Delta y}{t^2}$, calculated using the displacement (change in $y$) and time $t$ read directly from the height-vs-time graph.

In Period 3 Study Guide Question 15, during a head-on collision between two carts on a frictionless track, what are the average force $F_2$ and average acceleration $a_2$ on cart 2?

$F_2 = F_1$ (by Newton's Third Law, action-reaction forces are equal in magnitude) and $a_2 = \frac{F_2}{m_2}$.

In Period 3 Study Guide Question 16, at what time does an object change its direction of motion if its velocity is modeled by $v = (4.2\,\text{m/s}) - (1.4\,\text{m/s}^2)t$?

$t = 3.0\,\text{s}$ (Set velocity to zero: $0 = 4.2 - 1.4t \implies t = 3.0\,\text{s}$).

In Period 3 Study Guide Question 17, what is the correct expression for the tension force $T$ in a rope supporting a ball in a conical pendulum at angle $\theta$ with the vertical pole?

$T = \frac{mg}{\cos(\theta)}$ (Balancing vertical forces: $T \cos(\theta) = mg$).

In Period 3 Study Guide Question 19, when two blocks on a ramp are released touching (Trial 1) vs separated by a compressed spring (Trial 2), how do the net force on the system and the force on Block 1 compare?

Net force on the system is the same; force on block 1 is different.

In Period 3 Study Guide Question 20, a vertical spring launcher on a block sliding right at constant speed shoots a ball upward. Where is the ball when it reaches maximum height relative to the launcher?

Directly above the spring launcher (both maintain the same horizontal velocity component $v_x$).

In P12 Test Booklet Question 1, how does the tension force compare between Case A and Case B when String 2 is attached to the ceiling at a smaller angle to the vertical?

(C) $T_{1A} = T_{1B}$, because the horizontal component of tension in Case B is smaller.

In P12 Test Booklet Question 2, how is a car's acceleration determined from the recorded velocity graph?

(B) $\frac{v_f - v_i}{t_f - t_i}$ calculated using the slope of the velocity curve.

In P12 Test Booklet Question 3, what describes the car's speed and acceleration from the position and velocity graphs?

(C) Speeding increasing; Acceleration negative.

In P12 Test Booklet Question 4, a cart on a ramp has $v = 2.0\,\text{m/s}$ in the $+x$-direction at $t = 0$ and constant acceleration of $0.50\,\text{m/s}^2$ in the $-x$-direction. What describes its motion at $t > 4\,\text{s}$?

(D) The cart is traveling in the $-x$-direction and is speeding up.

In P12 Test Booklet Question 5, an object slides from rest down a frictionless air track tilted at angle $\theta$. How can the value of $\theta$ best be determined from position and time data?

(D) The slope of a graph of position as a function of the square of time.

In P12 Test Booklet Question 6, what is the magnitude of the average braking force on the $1500\,\text{kg}$ car based on the braking performance data?

(C) $12{,}000\,\text{N}$

In P12 Test Booklet Question 7, a passenger rolls a ball backward at $v_0$ on a train moving forward at $v_0$, and another passenger stops the ball on the table. What does the ball's velocity graph relative to the ground show?

(A) Graph showing $v = 0$ while rolling, then jumping to $+v_0$ when stopped on table.

In P12 Test Booklet Question 8, a $0.30\,\text{kg}$ toy robot pushes a $0.20\,\text{kg}$ toy doll with a force of $0.30\,\text{N}$ on a frictionless surface. What is the magnitude of the acceleration of the robot?

(C) $1.0\,\text{m/s}^2$

In P12 Test Booklet Question 9, a $1.0\,\text{kg}$ block on a flat table is connected over a frictionless pulley to a hanging $2.0\,\text{kg}$ block. What is the acceleration of the $2.0\,\text{kg}$ block?

(B) $3.3\,\text{m/s}^2$

In P12 Test Booklet Question 10, a board is held by two vertical springs ($k = 10{,}000\,\text{N/m}$ each). How far will each spring stretch when a $30\,\text{kg}$ person sits on the board in equilibrium?

(B) $0.015\,\text{m}$

In P12 Test Booklet Question 11, what must be true for a cart entering a vertical loop of radius $R$ with speed $v$ to remain on the track when it reaches point P?

(A) The net force exerted on the cart must be less than the force that total exerts on the cart.

In P12 Test Booklet Question 12, a ball of mass $m$ rotates in a horizontal circle supported by two taut strings forming a right triangle with a vertical rod. What is the tension $T_1$ in the upper string?

(C) $T_1 = \frac{mg}{\cos(\theta)}$

In P12 Test Booklet Question 13, which vectors represent the forces on a ball swinging in a horizontal circle on a string attached to a vertical pole?

(A) Diagram showing tension vector pointing up and inward along string and gravity vector pointing straight down.

In P12 Test Booklet Question 14, what claim is true regarding the force exerted on an astronaut by Earth in a space station orbiting at height $h$?

(D) The force exerted on the astronaut by Earth is equal to the gravitational force of the space station that is exerted on the astronaut; the two equal forces balance to cause the astronaut to float.

In P12 Test Booklet Question 15, what does the free-body diagram show for a $2\,\text{kg}$ object thrown upward on Planet X while it is in free fall?

(A) Free-body diagram showing a single downward vector of magnitude $F_{\text{Gravity}} = 2\,\text{N}$.

In P12 Test Booklet Question 16, if upward is positive and the floor's force on a bouncing ball spikes upward, what graph represents the force exerted on the floor by the ball?

(B) Graph showing force spiking upward during contact time, zero before and after.

In P12 Test Booklet Question 17, what is the magnitude of the gravitational field near the surface of Planet X if it has twice Earth's mass and three times Earth's radius?

(A) $2\,\text{N/kg}$

In P12 Test Booklet Question 18, Satellite A orbits Earth with speed $v_A$. What is the speed of Satellite B if its orbital radius is nine times that of Satellite A?

(B) $\frac{v_A}{3}$

In P12 Test Booklet Question 19, what forces appear on the free-body diagrams for Block X (table) and Block Y (hanging) connected over a pulley?

(A) Diagrams showing Block X with horizontal tension $T$ right, normal force up, gravity down; Block Y with tension up and gravity $2Mg$ down.

In P12 Test Booklet Question 20, when Block X (mass $M$ on table) is connected over a pulley to Block Y (mass $2M$ hanging), in which direction does the center of mass move, and what is the acceleration of Block X?

(A) Center of Mass moves Down and to the right ; Acceleration of Block X is $\left(\frac{2}{3}\right)g$.