Force and Motion

Which of the following statements is most closely associated with Newton's Third Law of Motion?

(A) "What goes up must come down."

(B) "For every action force, there is an equal but opposite reaction force."

(C) "An object at rest remains at rest."

(D) "The acceleration of an object is directly proportional to the force acting on the object but inversely proportional to the mass of the object."

(E) "The Universe tends toward disorder."

Three blocks, labeled A,B, and C, remain at rest on a table. The magnitude of the gravitational force on each block is indicated on the figure. What is the magnitude of the contact force on block C from block B?

(A) 1.0 N

(B) 6.0 N

(C) 7.0 N

(D) 12.0 N

(E) 13.0 N

A ball of mass $m=0.100 kg$ is launched straight upward so that it rises to a maximum height of 12.0 $m$ above the launch point. Ignore air resistance.

6. When the ball reaches its maximum height, which one of the following choices best represents the magnitude of the net force acting on the ball?

(A) 0 $N$
(B) 0.100 $N$
(C) 1.00 $N$
(D) 10.0 $N$
(E) 12.0 $N$

7. Approximately how much time does it take the ball to reach the maximum height from its launch?

(A) 0.65 $s$
(B) 1.10 $s$
(C) 1.20 $s$
(D) 1.55 $s$
(E) 2.40 $s$

A string of negligible mass connects an object of mass $M=10kg$ to the ceiling of an elevator. The elevator experiences a constant downward speed of 3.0 $m/s.$ Let $T$ represent the magnitude of the force on the mass $M$ by the string (tension), $G$ represent the magnitude of the gravitational force by the Earth acting on the mass $M$ hanging in the elevator, and $F$ represent the magnitude of the net force acting on the mass $M.$ Which one of the following choices describes the relationships between these forces?

(A) $F<T<G$

(B) $F=G=T$

(C) $F<G<T$

(D) $F=T<G$

(E) $F<T=G$

A 5.0 $kg$ mass moves along the $x$-axis. At one instant of time, the mass has position 2.0 $m$, velocity 3.0 $m/_{s}$, and acceleration 4.0 $m/s^{2}$. What is the net force acting on the mass at this instant of time?

(A) $0N$
(B) 10.0 $N$
(C) 15.0 $N$
(D) 20.0 $N$
(E) 22.5 $N$

A physics book sits at rest on a table. On top of the book is a calculator, also at rest. Which one of the following choices is the Newton's Third Law pair force to the force that the table exerts on the book?

(A) The contact force on the table by the book.

(B) The gravitational force on the book by the Earth.

(C) The gravitational force on the combination of the book and calculator by the Earth.

(D) The contact force on the book by the calculator.

(E) The contact force on the table by the ground supporting it.

A4.0 $kg$ object is pushed to the right on a rough surface by a horizontal force of15 $N$ as shown. During the push, the object accelerates uniformly to the right at 2.50 $m/s^{2}$. What must be the magnitude of the force of friction also acting on the object during the push?

(A) 0N
(B) 5N
(C) 10N
(D) 15N
(E) 25N

A string of negligible mass connects an object of mass $M=10kg$ to the ceiling of an elevator. The elevator experiences a constant downward acceleration of magnitude 6.0 $m/s^{2}.$ Let $T$ represent the magnitude of the force by the string (tension) acting on the mass $M$, let $G$ represent the magnitude of the gravitational force by the Earth acting on the mass $M$, and let $F$ represent the magnitude of the net force acting on the mass $M.$

Which one of the following choices describes the relationships between these forces?

(A) $T=G=F$

(B) $F<G<T$

(C) $T=F<G$

(D) $F<T=G$

(E) $T<F<G$

A constant force $F=50N$ (as shown in the figure) is applied for the 6.0 meter motion of the box upward along the incline. The mass of the block is $M=15kg$. Which one of the following choices best represents the work done by the force $F$ on the box for the motion?

(A) $300J$
(B) $282J$
(C) $260J$
(D) 193 $J$
(E) 150 $J$

An object of mass $M$ is dropped fr om a height $H$ above the ground. The object bounces off of a horizontal surface in a collision lasting time $T$. The object then rises upward to a maximum height $H/2$. What was the magnitude of the average net force acting on the mass during the collision with the surface?

(A) $(2-\displaystyle \sqrt{2})\frac{M\sqrt{gH}}{T}$
(B) $(\displaystyle \frac{1}{\sqrt{2}}+1)\frac{M\sqrt{gH}}{T}$
(C) $(\displaystyle \sqrt{3})\frac{M\sqrt{gH}}{T}$
(D) $(2\displaystyle \sqrt{2}-1)\frac{M\sqrt{gH}}{T}$
(E) $(\displaystyle \sqrt{2}+1)\frac{M\sqrt{gH}}{T}$

A block initially moving at 8.0 $m/s$ accelerates uniformly to rest on a horizontal surface. The block travels a distance of 12.0 $m$ during the slide. Which one of the following choices best represents the coefficient of kinetic friction between the surface and the block?

(A) 1.20
(B) 0.667
(C) 0.533
(D) 0.267
(E) 0.133

Which one of the following choices correctly identifies all of the listed situations for which there is a non-zero acceleration?

Situation I : A point object moves in a straight line with increasing speed.

Situation II : A point object moves in a circular path with constant speed.

Situation III: A point objects moves in a circular path with decreasing speed.

(A) Situations I, II, & III
(B) Only Situations I & III
(C) Only Situations II & III
(D) Only Situation III
(E) Only Situation I

Three equal masses are suspended from a classroom ceiling by a series of strings as shown in the figure. Which string has the greatest tension?

(A) Only String A

(B) Only String $\mathrm{B}$

(C) Only String $\mathrm{C}$

(D) Strings $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ have the same non-zero tension.

(E) Strings $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ all have no tension.

A box of mass 5.0 $kg$ is being pushed to the right across a horizontal surface while a constant frictional force of 8.0 $N$ acts on the box. At some instant o ftime, the box has a speed of $4.0\displaystyle \frac{m}{s}$ and an acceleration of $3.0\displaystyle \frac{m}{s^{2}}.$ What is the magnitude of the net force acting on the box at this instant?

(A) 7.0 $N$
(B) 12.0 $N$
(C) 15.0 $N$
(D) 20.0 $N$
(E) 23.0 $N$

Which one of the following scientists is most associated with the following statement: “For small displacements of an object from equilibrium, there is a restoring force that is proportional to the displacement.”?

(A) Einstein
(B) Hooke
(C) Huygens
(D) Kepler
(E) Lenz

A box rests on the floor of an elevator. The elevator is accelerating upward. Which one of the following choices best represents the Newton's Third Law pair force to the gravitational force acting on the box by the Earth?

(A) There is no Newton's Third Law pair force in this scenario.

(B) The entire normal force of contact from the floor on the box.

(C) Only a portion of the normal force of contact from the floor on the box.

(D) The force of the cables pulling upward on the elevator.

(E) The gravitational force acting on the Earth by the box.

A uniform block of mass $m$ is placed on an inclined plane of angle $\theta$. When released, the block does not move. It is determined that the normal force acting from the incline on the block has a magnitude of 62 $N$ while the force of static friction acting on the block has a magnitude of 38 $N$. The coefficient of static friction between the block and inclined plane is $\mu_{s}=0.92$. Which one of the following choices best represents the mass, $m$, of the block?

(A) 2.4 $kg$
(B) 6.2 $kg$
(C) 7.3 $kg$
(D) 8.4 $kg$
(E) 10.0 $kg$

In the figure shown, the mass $m=6.0kg$ and the mass $M=14.0kg$ are stationary. The mass $M$ rests on the floor. Which one of the following choices represents the tension in the string connecting the masses?
(A) 40 $N$
(B) 60 $N$
(C) 80 $N$
(D) 140 $N$
(E) 200 $N$

A person wishes to accelerate an object upward uniformly. Which one of the following choices must be true of the force, $F$, provided by the person onto the object? $W$ represents the magnitude of the gravitational force acting on the object. Ignore any effects of the air or of the Earth's rotation.

(A) $F=W$
(B) $F\geq W$
(c) $F>W$
(D) $F\geq 2W$
(E) $F>2W$

A block is suspended in the air at the end of a string held by a person. The person pulls on the string uniformly accelerating the block upward for a short time. During this time, which one of the following choices correctly identifies the Newton's Third Law pair force to the force of the string on the block?

(A) the gravitational force from the Earth on the block

(B) the force from the string on the person

(C) the force from the person on the string

(D) the force from the block on the string

(E) the force from the person on the block

Two blocks $X$ and $Y$ are in contact on a frictionless horizontal surface. A constant 35 $N$ force is applied to the right onto block $X.$ What is the magnitude of the force that block $Y$ exerts onto block $X$?

(A) 35 $N$
(B) 28 $N$
(C) 25 $N$
(D) 14 $N$
(E) 10 $N$

A box slides with uniform acceleration up an incline. The box has an initial speed of $9.0\displaystyle \frac{m}{s}$ and rises vertically 2.60 $m$ before coming to rest. If the angle of the incline is $30^{\circ}$, what is the coefficient of kinetic friction between the box and the incline?

(A) 0.298
(B) 0.322
(C) 0.372
(D) 0.483
(E) 0.557

A small object of mass $M$ is released from rest at the top of a frictionless incline. The incline has a mass $\mathrm{M}$ and makes an angle $\theta$ with the horizontal. The incline remains at rest on a table as the small object slides. During the slide, what is the magnitude of the normal force from the table on the incline?

(A) $2Mg(1-\tan\theta)$
(B) $2Mg(1-\sin\theta)$
(C) $2Mg$
(D) $Mg(2-\sin^{2}\theta)$
(E) $Mg(2-\sin\theta)$

Three identical wood blocks are raced across three different flat surfaces, with the faces of the blocks on the surfaces. Each block is pulled horizontally with the same force $F$ from one edge by a light string attached to the block. Block 1 is pulled on a frictionless surface. Block 2 is pulled on a surface with a nonzero kinetic friction coefficient, and a zero static friction coefficient. Block 3 is pulled on a surface with a nonzero static friction coefficient, and the same kinetic coefficient as for Block 2, where $\mu_{k}<\mu_{s}$. If each block starts from rest and is pulled until traveling the same fixed horizontal distance, which of the following choices correctly ranks the times $(\mathrm{t}_{1},\ \mathrm{t}_{2},\ \mathrm{t}_{3})$ it takes for each block to traverse the distance?

(A) $t_{1}<t_{2}<t_{3}$
(B) $t_{1}=t_{2}=t_{3}$
(C) $t_{1}<t_{2}=t_{3}$
(D) $t_{3}<t_{2}<t_{1}$
(E) $t_{2}<t_{3}<t_{1}$

An Atwood machine is shown in the diagram at the right with $\mathrm{m}_{1}=0.60$ kg and $\mathrm{m}_{2}=0.40$ kg. What is the magnitude of the acceleration of $\mathrm{m}_{2}$? Ignore friction and the mass of the pulley.

(A) 4.2 $\mathrm{m}/\mathrm{s}^{2}$

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

(C) 2.0 $\mathrm{m}/\mathrm{s}^{2}$

(D) 5.0 $\mathrm{m}/\mathrm{s}^{2}$

(E) 1.0 $\mathrm{m}/\mathrm{s}^{2}$

A 30.0-N block falls straight down from a height of 10.0 $\mathrm{m}$, and strikes the ground with a velocity of 7.00 $\mathrm{m}/\mathrm{s}$. What average force of air friction acts on it as it falls?

(A) 22.65-N
(B) 45.45-N
(C) 75.0-N
(D) 206.5-N
(E) 293-N

Two boxes are stacked on a table as shown at right. The mass of box 1 is $m$ and the mass of box 2 is $3m$. The surface between box 2 and the table is smooth and the surface between the two boxes is rough. When a force, $F$, is applied, box 1 does not slide on box 2. What is the minimum coefficient of static friction between the boxes?

(A)$\displaystyle \frac{F}{4mg} \\ (\displaystyle \mathrm{B})\frac{F}{3mg} \\ (\displaystyle \mathrm{C})\frac{F}{2mg} \\ (\displaystyle \mathrm{D})\frac{F}{mg} \\ (\displaystyle \mathrm{E})\frac{2mg}{F}$

An object of mass $m$ initially at rest experiences a uniform, non-zero acceleration. Which of the following statements is correct?
(A) The object's displacement is directly proportional to its time of travel.
(B) The object's velocity is directly proportional to its time of travel.
(C) The object's acceleration is directly proportional to its time of travel.
(D) The object's kinetic energy is directly proportional to its time of travel.
(E) The net force acting on the object is directly proportional to its time of travel.

A car is moving along a straight horizontal road at a speed of $20 \mathrm{~m} / \mathrm{s}$. The brakes are applied and a constant force of 5000 N brings the car to a stop in 10 s . What is the mass of the car?
(A) 1250 kg
(B) 2500 kg
(C) 5000 kg
(D) 7500 kg
(E) 10,000 kg

Two forces have magnitudes of 11.0 N and 5.0 N . The magnitude of their sum could NOT be equal to which of the following values?
(A) 16.0 N
(B) 9.0 N
(C) 7.0 N
(D) 5.0 N
(E) 6.0 N

A refrigerator has a mass of 150 kg and rests in the open back end of a delivery truck. If the truck accelerates from rest at $1.5 \mathrm{~m} / \mathrm{s}^{2}$, what is the minimum coefficient of static friction between the refrigerator and the bed of the truck that is required to prevent the refrigerator from sliding off the back of the truck?
(A) 0.08
(B) 0.10
(C) 0.12
(D) 0.15
(E) 0.18

Three blocks ( $m_{1}=1 \mathrm{~kg}, m_{2}=2 \mathrm{~kg}$, $m_{3}=3 \mathrm{~kg}$ ) connected by cords are pulled by a constant force, $F$, of 18 N on a frictionless horizontal table. $T_{2}$ is the tension in the rope between $m_{2}$ and $m_{3}$. What is $T_{2}$ ?

(A) 3 N
(B) 6 N
(C) 9 N
(D) 12 N
(E) 15 N

A 3.00 kg bucket of water is raised with an upward acceleration of $2.20 \mathrm{~m} / \mathrm{s}^{2}$ from a well by means of an attached rope. What is the tension in the rope?
(A) 30.2 N
(B) 33.3 N
(C) 36.6 N
(D) 39.0 N
(E) 43.2 N

A shipping box in a warehouse has a mass of 2.00 kg and slides down an inclined plane that makes an angle of $30^{\circ}$ with the horizontal. The coefficient of kinetic friction between the box and the plane surface is 0.866 . How much force (parallel to the incline) should be applied to the box so that it moves down the plane at constant speed?
(A) 5.00 N
(B) 6.50 N
(C) 3.80 N
(D) 4.60 N
(E) 11.0 N

To break a board, a typical karate chop delivers 3000 N of force to the board. The force that the board exerts on the hand during the chop is
(A) less than 3000 N .
(B) 3000 N .
(C) greater than 3000 N .
(D) dependent upon the type of wood.
(E) dependent upon the speed of the karate chop.

A force applied to a rocket gives it an upward acceleration equal to 2 times the acceleration of gravity. The magnitude of the force is equal to:
(A) One-half the weight of the rocket
(B) The weight of the rocket
(C) Two times the weight of the rocket
(D) Three times the weight of the rocket
(E) Four times the weight of the rocket

Three vector forces $F_{1}, F_{2}$, and $F_{3}$ act on a particle that has a mass of 3.00 kg as shown in in the diagram at right. What is the particle's acceleration?

(A) $9.49 \mathrm{~m} / \mathrm{s}^{2}$
(B) $9.59 \mathrm{~m} / \mathrm{s}^{2}$
(C) $9.69 \mathrm{~m} / \mathrm{s}^{2}$
(D) $9.79 \mathrm{~m} / \mathrm{s}^{2}$
(E) $9.89 \mathrm{~m} / \mathrm{s}^{2}$

A block with a mass of 1.5 kg is at rest on a ramp as shown at right. The ramp is angled at $50^{\circ}$ to the horizontal and has a rough surface with coefficients of static and kinetic frictions that are $\mu_{\mathrm{s}}=0.65$ and $\mu_{\mathrm{k}}=0.3$, respectively. The block is being held in place by a spring with $k=40 \mathrm{~N} / \mathrm{m}$. What is the minimum distance the spring must be stretched in order for the block to be at rest?

(A) 0.043 m
(B) 0.053 m
(C) 0.13 m
(D) 0.17 m
(E) 0.21 m

A hockey puck is given an initial speed of $10.0 \mathrm{~m} / \mathrm{s}$. It slides 50.0 m on the ice before it stops. What is the coefficient of kinetic friction between the puck and the ice?
(A) 0.090
(B) 0.10
(C) 0.11
(D) 0.12
(E) 0.13

A wooden crate is placed on a flat surface, and three forces act on it: $F_{1}$ is applied horizontally to the right, $F_{2}$ is applied horizontally to the left, and $F_{3}$ is applied vertically down. Consider the following statements for this situation:
Statement I: If $F_{1}>F_{2}$, the crate with move to the right.
Statement II: The net force acting on the crate is the vector sum of $F_{1}, F_{2}, \& F_{3}$.
Statement III: If $F_{3}>F_{1}+F_{2}$, the crate will move upward.
Which statement(s) accurately describe(s) the result of the forces acting on the crate?
(A) I only
(B) II only
(C) I & II only
(E) II & III only

At a construction site, a bulldozer drags a log weighing 500 N along a rough, horizontal surface. The cable attached to the log makes an angle of $30.0^{\circ}$ with the ground. The coefficient of static friction between the log and the ground is 0.500 . What minimum tension is required in the cable for the log to begin to move?
(A) 125 N
(B) 224 N
(C) 289 N
(D) 500 N
(E) 577 N

An Atwood's machine has two masses $m_{1}$ and $m_{2}$ connected by a light string passing over a pulley. If $m_{1}=5 \mathrm{~kg}$ and $m_{2}=7 \mathrm{~kg}$, and the pulley has a radius of 0.1 m , what is the tension in the string?
(A) 20.2 N
(B) 58.4 N
(C) 81.7 N
(D) 120.0 N
(E) 140.0 N

A rope is used to connect two boxes, one with a mass of $m$ and the other with a mass of $2 m$ as shown in the diagram at the right. The boxes are resting on a smooth surface. A force $F$ is then applied to the larger box. What is the tension in the connecting rope?
(A) 3F
(B) F
(C) F/2
(D) F/3
(E) 2F

A simple pendulum is hanging from the ceiling of a train car. It is observed to hang at $10^{\circ}$ to the right of vertical. Which of the following could describe this observation?
(A) The train car is at rest.
(B) The train car is accelerating to the left.
(C) The train car is moving with constant velocity to the left.
(D) The train car is accelerating to the right.
(E) The train car is moving with constant velocity to the right.

A shopping cart with a speed of $v_{0}$ is brought to rest by an applied force. If the time interval over which the force is applied is increased, then bringing the cart to rest requires
(A) a smaller force.
(B) the same force.
(C) a larger force.
(D) another applied force acting in the same direction as the original applied force.
(E) a frictional force opposing the cart's motion.

A box of mass $m$ is given an initial speed $v$ and slides along a horizontal surface. The coefficient of kinetic friction between the box and the surface is $\mu$. The box stops after sliding a distance $d$. The stopping distance, $d$, would be doubled if which of the following quantities were doubled?
(A) only the mass of the box.
(B) only the initial speed of the box.
(C) only the coefficient of friction between the box and the surface.
(D) only the mass of the box and the coefficient of friction between the box and the surface.
(E) only the initial speed of the box and the coefficient of friction between the box and the surface.

A fan cart with an initial velocity is located on a level track with an initial position as shown.

The cart's fan is blowing air to the right. Which of the following position versus time graphs corresponds to the cart's subsequent motion?

A $50-\mathrm{kg}$ person stands on a bathroom scale inside of an elevator. The scale reads 400 N . Which of the following could describe how the elevator is moving?
(A) The elevator is moving up while decreasing speed at a rate of $2 \frac{m}{s^{2}}$.
(B) The elevator is moving up while increasing speed at a rate of $2 \frac{m}{s^{2}}$.
(C) The elevator is moving up at a constant speed of $2 \frac{m}{s}$.
(D) The elevator is moving down while decreasing speed at a rate of $2 \frac{m}{s^{2}}$.
(E) The elevator is moving down at a constant speed of $2 \frac{m}{s}$.

A bike and rider with a combined mass of 70 kg ride through a curve of radius of 20 m at a speed of $11 \frac{\mathrm{~m}}{\mathrm{~s}}$. The road is wet and the coefficient of static friction between the road and the tires is 0.50 . Which of the following correctly explains whether the bike and rider will slip and why.
(A) The bike slips because the maximum speed the bike can go around the curve without slipping is $10 \mathrm{~m} / \mathrm{s}$.
(B) The bike slips because the force the tires exert on the road is greater than the friction component of the force the road exerts on the tires.
(C) The bike does not slip because the maximum speed the bike can go around the curve without slipping is $15 \mathrm{~m} / \mathrm{s}$.
(D) The bike does not slip because the force the tires exert on the road is less than the friction component of the force the road exerts on the tires.
(E) The bike does not slip because the coefficient of static friction is too large.

An airplane is flying in a vertical loop. At the bottom of the loop, the forces on the pilot are such that...
(A) $\mathrm{F}_{\mathrm{N}}>\mathrm{F}_{\mathrm{g}}$.
(B) $\mathrm{F}_{\mathrm{N}}=\mathrm{F}_{\mathrm{g}}$.
(C) $\mathrm{F}_{\mathrm{N}}<\mathrm{F}_{\mathrm{g}}$.
(D) $\mathrm{F}_{\mathrm{N}}$ cannot be determined without knowing the plane's speed.
(E) $\mathrm{F}_{\mathrm{g}}$ decreases.

An object with mass $M$ moves due East on a frictionless horizontal surface with a speed of $V$. A second object of mass $\frac{1}{2} M$ has a speed of $3 V$. The two objects collide and stick together. If the objects are moving due South after the collision, with what speed are they moving?
(A) $\frac{5}{3} V$
(B) $\frac{1}{3} V$
(C) $\frac{\sqrt{5}}{3} \mathrm{~V}$
(D) $\frac{4 \sqrt{2}}{3} \mathrm{~V}$
(E) $\frac{\sqrt{33}}{3} V$