AP Physics 1 Full-length practice exam 1

A solid metal sphere of mass $1.0\text{kg}$ and density $4000{\text{kg/m}}^3$ is fully submerged in water. With $g=10{\text{m/s}}^2$, what is the apparent weight (the reading on a scale supporting it under water)?

A uniform meterstick (mass $0.20\text{kg}$) is balanced at its center. A $0.10\text{kg}$ mass is hung $30\text{cm}$ from the pivot on one side. Where on the other side should a $0.30\text{kg}$ mass be hung to balance the stick?

The velocity-vs-time graph of a moving object is a straight line that starts at $v=-4\text{m/s}$ at $t=0$ and reaches $v=+6\text{m/s}$ at $t=5\text{s}$. What is the average acceleration over this interval?

A pendulum on Earth has period $T_E$. If you take it to a planet where gravity is one-fourth Earth's gravity, what is its new period?

Two students start from the same point. Student A runs at a constant $4.0\text{m/s}$. Student B starts from rest at the same instant and accelerates uniformly at $2.0{\text{m/s}}^2$. How long after the start does Student B catch up with Student A?

A block of mass $m$ slides down a frictionless ramp from height $h$. At the bottom it enters a horizontal surface with kinetic friction coefficient $\mu$. How far along the horizontal surface does the block slide before stopping?

A wooden block floats in water with $80\%$ of its volume submerged. What is the density of the wood?

A $0.10\text{kg}$ ball hits a wall at $20\text{m/s}$ and rebounds at $15\text{m/s}$ (opposite direction). The collision lasts $0.020\text{s}$. What is the average force the wall exerts on the ball?

A simple pendulum of length $L=1.0\text{m}$ swings near Earth's surface ($g=10{\text{m/s}}^2$). What is its approximate period?

A $2.0\text{kg}$ block sits on a horizontal surface with coefficient of static friction ${\mu }_s=0.40$. Taking $g=10{\text{m/s}}^2$, what is the maximum horizontal force that can be applied without the block sliding?

A heavy door is harder to push open if you push close to the hinge. The reason is that:

Two identical containers each hold the same volume of fluid: container 1 has water (density $1000{\text{kg/m}}^3$), container 2 has oil (density $800{\text{kg/m}}^3$). Both fluids fill their containers to the same height. Compare the pressure at the bottom of each container.

A projectile is launched from ground level at a speed of $30\text{m/s}$ at an angle of $30°$ above the horizontal. Taking $g=10{\text{m/s}}^2$ and ignoring air resistance, how long is the projectile in the air before returning to the ground?

Two students compare their commutes. Student X drives the first half of the distance at $30\text{m/s}$ and the second half at $60\text{m/s}$. Student Y drives the first half of the time at $30\text{m/s}$ and the second half of the time at $60\text{m/s}$. Which student has the larger average speed for the trip?

A cube of side $0.10\text{m}$ is fully submerged in water (density $\rho =1000{\text{kg/m}}^3$). With $g=10{\text{m/s}}^2$, what is the buoyant force on the cube?

Which of the following collisions conserves both momentum AND kinetic energy?

A wheel rotating at $10\text{rad/s}$ slows uniformly to rest in $5.0\text{s}$. Through what angle does it rotate during this time?

A $0.50\text{kg}$ mass on a spring oscillates with angular frequency $\omega =4.0\text{rad/s}$. What is the spring constant?

An object hangs from a spring scale inside an elevator. When the elevator is at rest the scale reads $50\text{N}$. When the elevator accelerates upward at $2.0{\text{m/s}}^2$ (with $g=10{\text{m/s}}^2$), what does the scale read?

A spinning ice skater has angular momentum $L$ and rotational kinetic energy $KE$. By pulling in his arms, he reduces his moment of inertia by half. What are the new $L$ and $KE$?

A force of $20\text{N}$ is applied perpendicular to the end of a $0.50\text{m}$ wrench. What torque does it produce about the bolt?

A spring with spring constant $k=200\text{N/m}$ is compressed $0.10\text{m}$ from its natural length. How much potential energy is stored in the spring?

Where in its motion does a simple harmonic oscillator have its maximum acceleration?

A $2.0\text{kg}$ object on a string moves in a horizontal circle of radius $0.50\text{m}$ at $4.0\text{m/s}$. What is the tension in the string?

A solid disk of moment of inertia $I=0.20{\text{kg⋅m}}^2$ spins at angular speed $\omega =10\text{rad/s}$. What is its rotational kinetic energy?

Cart A ($2\text{kg}$, $3\text{m/s}$ east) collides with Cart B ($4\text{kg}$, $1\text{m/s}$ west) on a frictionless track. After they stick together, what is the velocity of the combined carts?

A horizontal force of $20\text{N}$ pushes a box $5.0\text{m}$ across a level floor. How much work does the force do on the box?

A $500\text{kg}$ roller-coaster car at the top of a $40\text{m}$ hill is moving at $5.0\text{m/s}$. With $g=10{\text{m/s}}^2$ and ignoring friction, what is its speed at the bottom of the hill?

A stone is dropped from a tall cliff. Ignoring air resistance and taking $g=10{\text{m/s}}^2$, how far does it fall during the third second of its fall (between $t=2\text{s}$ and $t=3\text{s}$)?

An object moves in uniform circular motion. Which statement about the net force is true?

A $5.0\text{kg}$ block on a frictionless horizontal surface is pulled by a horizontal force of $20\text{N}$. What is the block's acceleration?

A wheel of moment of inertia $I=0.50{\text{kg⋅m}}^2$ has a constant net torque of $2.0\text{N⋅m}$ applied for $4.0\text{s}$ starting from rest. What is its angular momentum at $t=4.0\text{s}$?

A $1500\text{kg}$ car rounds a flat (unbanked) curve of radius $50\text{m}$ at $15\text{m/s}$. What is the minimum coefficient of friction needed to keep the car on the curve? (Take $g=10{\text{m/s}}^2$.)

Two masses, $m_1=2.0\text{kg}$ and $m_2=3.0\text{kg}$, are connected by a massless string over a frictionless pulley (Atwood machine). With $g=10{\text{m/s}}^2$, what is the magnitude of acceleration of the system?

Two balls of equal mass collide elastically head-on. Ball A moves at $+5\text{m/s}$, Ball B at $-3\text{m/s}$. What are their velocities after the collision?

A swimming pool is $4.0\text{m}$ deep. With ${\rho }_{water}=1000{\text{kg/m}}^3$, $g=10{\text{m/s}}^2$, and atmospheric pressure $P_0=1.0\times 10^5\text{Pa}$, what is the absolute pressure at the bottom?

A solid disk of mass $M$ and radius $R$ rotates about an axis through its center. What is its moment of inertia?

A $1000\text{kg}$ elevator rises at a constant $2.0\text{m/s}$. Taking $g=10{\text{m/s}}^2$, what is the minimum power the motor must deliver?

Water flows through a horizontal pipe. At point 1 the pressure is $2.0\times 10^5\text{Pa}$ and the speed is $3.0\text{m/s}$. At point 2 the speed has increased to $5.0\text{m/s}$. With $\rho =1000{\text{kg/m}}^3$, what is the pressure at point 2?

An object's position as a function of time is shown in a graph (not reproduced here): position is constant at $x=4\text{m}$ for $0\le t<2\text{s}$, then increases linearly to $x=10\text{m}$ at $t=5\text{s}$, then decreases linearly back to $x=4\text{m}$ at $t=8\text{s}$. What is the object's average velocity over the interval from $t=0$ to $t=8\text{s}$?

A car traveling at $20\text{m/s}$ brakes uniformly and stops in $4.0\text{s}$. What is the magnitude of its acceleration?

An object moves along the x-axis with the position function $x(t)=3t^2-12t+5$ (meters, with $t$ in seconds). At what time does the object momentarily come to rest?

A net torque of $4.0\text{N⋅m}$ is applied to a wheel with moment of inertia $I=2.0{\text{kg⋅m}}^2$. What is the angular acceleration?

A hydraulic press has a small piston of area $A_1=0.010{\text{m}}^2$ and a large piston of area $A_2=0.50{\text{m}}^2$. If a force of $200\text{N}$ is applied to the small piston, what force is exerted on the large piston?

A child of mass $m$ jumps onto the edge of a stationary merry-go-round (a disk of mass $M$ and radius $R$ on a frictionless bearing) with tangential speed $v$. What is the angular speed of the system after the child lands?

Water flows through a pipe whose cross-sectional area decreases from $A_1=4{\text{cm}}^2$ to $A_2=1{\text{cm}}^2$. If the speed in the wider section is $0.50\text{m/s}$, what is the speed in the narrow section?

A $2.0\text{kg}$ object's speed increases from $3.0\text{m/s}$ to $5.0\text{m/s}$. What is the net work done on the object?

A $1.0\text{kg}$ cart moving at $4.0\text{m/s}$ collides and sticks to a $3.0\text{kg}$ cart at rest. What is the speed of the combined carts after the collision?

A car accelerates uniformly from rest. After traveling $20\text{m}$, its speed is $10\text{m/s}$. What is its speed after it has traveled an additional $60\text{m}$ (i.e., $80\text{m}$ total)?

Which of the following statements about work is correct?