Practice Test 1 - AP Physics 1

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A $3.0\,\text{kg}$ cart moving right at $2.0\,\text{m/s}$ collides and sticks to a $1.0\,\text{kg}$ cart initially at rest on a frictionless track. The system is both carts, and external forces are negligible during the collision. What is the final velocity of the combined carts?
2. A cart is attached to an ideal spring. Equilibrium is $x=0$ at the relaxed length; rightward is positive. The cart is at $x=+0.03\,\text{m}$ and then at $x=+0.09\,\text{m}$. The spring force magnitude changes by a factor of
3. A door is held open at rest by two forces applied at different points: one student pushes near the knob while another pushes near the hinge. The door does not rotate, and the angular acceleration is $\alpha=0$. What must be true about the net torque on the door about the hinge axis?
4. Two asteroids interact gravitationally far from any planets. Asteroid $X$ has mass $2m$ and asteroid $Y$ has mass $m$, separated by distance $r$. They are then repositioned so the distance remains $r$ but $X$ is replaced by an asteroid of mass $4m$. Compared with the original gravitational force magnitude, the new force magnitude is
5. A $1.0\,\text{kg}$ cart moving east at $5.0\,\text{m/s}$ collides head-on and sticks with a $4.0\,\text{kg}$ cart moving west at $1.0\,\text{m/s}$. Define the system as both carts; external forces are negligible. What is the final velocity of the combined carts?
6. A student on a low-friction cart pulls a rope attached to a second cart; for the two carts as the system, what is true about center-of-mass motion?
7. A $1.5\,\text{kg}$ block moving left receives a rightward impulse of $3.0\,\text{N}\cdot\text{s}$. Which statement about $\Delta \vec p$ is correct?
8. A $0.10\,\text{kg}$ cart moving right at $10\,\text{m/s}$ collides and sticks to a $0.40\,\text{kg}$ cart initially at rest. Consider both carts as the system and assume external forces are negligible during the collision. What is the speed of the combined carts immediately after?
9. A $0.10\,\text{kg}$ ball moving right at $8.0\,\text{m/s}$ strikes a $0.40\,\text{kg}$ cart initially at rest on a frictionless track and sticks in it. Define the system as ball + cart, and assume external forces are negligible during the collision. What is the final speed of the combined ball-cart system?
10. Two objects interact gravitationally. Case 1: masses $m$ and $m$ separated by $r$. Case 2: masses $2m$ and $m$ separated by $2r$. Which case has the greater gravitational force magnitude?
11. A constant force of $3\,\text{N}$ acts downward on a glider for $2.0\,\text{s}$. What is the magnitude of the glider's momentum change?
12. Two ice skaters stand on frictionless ice and push off each other. Define the system as both skaters together; the push forces they exert on each other are internal. A steady wind exerts a horizontal force to the east on both skaters (an external force on the system). Immediately after they push off, the skaters move apart while the wind continues. Which describes the motion of the system's center of mass?
13. A mass–spring oscillator moves without friction. The equilibrium position is at $x=0$. At $x=\pm A$, the mass is momentarily at rest so kinetic energy is $0$ and potential energy is maximum; at $x=0$, kinetic energy is maximum. Mechanical energy is conserved. The mass is at some position where the spring potential energy is $\tfrac{3}{4}$ of the total mechanical energy. At that position, what fraction of the total mechanical energy is kinetic energy?
14. Two identical pucks, each of mass $m$, slide on ice. Puck A moves at speed $2v$; puck B moves at speed $v$ in any direction. No friction acts. What is the ratio $K_A/K_B$ of their kinetic energies?
15. A pulley experiences a net torque of $2.5\,\text{N}\cdot\text{m}$ for $1.2\,\text{s}$. What is the change in angular momentum?
16. A satellite moves in a circular orbit around a planet. At point L, its velocity is tangent east. Which free-body diagram best represents forces on the satellite (neglect drag)?
17. A 2.0 kg book rests on a horizontal table. Friction is negligible. The book is pulled to the right by a horizontal string with tension 6.0 N, and it accelerates to the right. Which set of forces acts on the book? Stem: Which free-body diagram correctly represents the forces on the book?
18. Two rigid objects rotate about fixed axes through their centers. Object 1 has smaller $I$ but larger $\omega$ than Object 2. With no numbers given, which conclusion about their rotational kinetic energies is supported?
19. Two metal spheres have equal mass. Sphere X has a larger volume than sphere Y. Which comparison is correct?
20. A square plate can rotate about a pivot at its center. A force is applied at the midpoint of the top edge, directed straight toward the pivot (qualitatively: along the radius). The line of action passes through the pivot, giving a zero lever arm. What is the torque about the pivot?

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