AP-Style Practice QuestionsAP 风格练习题
Topics考点 4.1 - 4.4MECH
Show all supporting work on scratch paper. Each item is labeled with its Mechanics topic and whether a calculator is permitted on that AP Exam section. Take $g = 9.8~\mathrm{m/s^2}$ unless a problem says otherwise.请在草稿纸上写出所有辅助步骤。每题均标注力学考点及该 AP 考试模块是否允许使用计算器。除题目另有说明外，取 $g = 9.8~\mathrm{m/s^2}$。
A $0.50~\mathrm{kg}$ ball travels east at $4.0~\mathrm{m/s}$. The magnitude of its momentum is一个质量为 $0.50~\mathrm{kg}$ 的小球以 $4.0~\mathrm{m/s}$ 的速度向东运动。其动量大小为
A constant force of $10~\mathrm{N}$ acts on an object for $3.0~\mathrm{s}$. The magnitude of the impulse delivered to the object is一个 $10~\mathrm{N}$ 的恒力作用在某物体上，持续时间为 $3.0~\mathrm{s}$。该力对物体施加的冲量大小为
Two carts of equal mass sit at rest on a frictionless track, in contact with a compressed spring between them. After the spring is released, cart A moves left at $2.0~\mathrm{m/s}$. Cart B then moves两辆质量相等的小车静止在无摩擦轨道上，中间夹着一根压缩弹簧。弹簧释放后，小车 A 以 $2.0~\mathrm{m/s}$ 向左运动，则小车 B 的运动情况为
In which type of collision is the total kinetic energy of the system not conserved?在哪种碰撞类型中，系统的总动能不守恒？
A force exerted on a $2.0~\mathrm{kg}$ object varies linearly from $0$ at $t = 0$ to $20~\mathrm{N}$ at $t = 0.40~\mathrm{s}$, then drops back to $0$ at $t = 0.80~\mathrm{s}$ (a triangular pulse). The object starts at rest. Its speed at $t = 0.80~\mathrm{s}$ is作用在 $2.0~\mathrm{kg}$ 物体上的力从 $t = 0$ 时的 $0$ 线性增大到 $t = 0.40~\mathrm{s}$ 时的 $20~\mathrm{N}$，再降回 $t = 0.80~\mathrm{s}$ 时的 $0$（三角脉冲）。物体由静止开始，$t = 0.80~\mathrm{s}$ 时的速度大小为
A $0.20~\mathrm{kg}$ ball strikes a wall horizontally at $5.0~\mathrm{m/s}$ and rebounds straight back at $4.0~\mathrm{m/s}$. The magnitude of the impulse delivered by the wall to the ball is一个 $0.20~\mathrm{kg}$ 的小球以 $5.0~\mathrm{m/s}$ 水平撞墙，以 $4.0~\mathrm{m/s}$ 原路反弹。墙壁对小球施加的冲量大小为
A $3.0~\mathrm{kg}$ cart moving at $4.0~\mathrm{m/s}$ collides with and sticks to a stationary $1.0~\mathrm{kg}$ cart on a frictionless track. The speed of the combined carts immediately after the collision is一辆质量为 $3.0~\mathrm{kg}$ 、速度为 $4.0~\mathrm{m/s}$ 的小车在无摩擦轨道上与静止的 $1.0~\mathrm{kg}$ 小车碰撞并粘在一起。碰后两车合体的速度大小为
A $60~\mathrm{kg}$ skater stands at rest on frictionless ice and throws a $3.0~\mathrm{kg}$ ball horizontally at $8.0~\mathrm{m/s}$ relative to the ground. The skater's recoil speed is一名 $60~\mathrm{kg}$ 的溜冰者静止站在无摩擦冰面上，水平抛出一个 $3.0~\mathrm{kg}$ 的球，球相对地面的速度为 $8.0~\mathrm{m/s}$。溜冰者的反冲速度大小为
In a one-dimensional elastic collision, a moving puck strikes an identical stationary puck. Immediately after the collision,在一维弹性碰撞中，一个运动的冰球撞击一个相同质量且静止的冰球。碰撞后瞬间，
Two pucks of equal mass collide and stick together. Just before the collision, puck 1 moves east at $3.0~\mathrm{m/s}$ and puck 2 moves north at $4.0~\mathrm{m/s}$. Immediately after the collision, the speed of the combined object is两个质量相等的冰球碰撞后粘在一起。碰前，冰球 1 以 $3.0~\mathrm{m/s}$ 向东运动，冰球 2 以 $4.0~\mathrm{m/s}$ 向北运动。碰后合体的速度大小为
A $0.15~\mathrm{kg}$ baseball arrives at home plate moving horizontally at $40~\mathrm{m/s}$ and is hit straight back at $50~\mathrm{m/s}$. The contact between bat and ball lasts $1.5~\mathrm{ms}$. The magnitude of the average force exerted by the bat on the ball is closest to一个 $0.15~\mathrm{kg}$ 的棒球以 $40~\mathrm{m/s}$ 水平飞向本垒板，被击后以 $50~\mathrm{m/s}$ 原路返回。球棒与球的接触时间为 $1.5~\mathrm{ms}$。球棒对球施加的平均力大小最接近
Two carts of equal mass collide head-on at the same speed and stick together. Compared with the total kinetic energy before the collision, the total kinetic energy immediately after the collision is两辆质量相等的小车以相同速度正面碰撞并粘在一起。与碰前总动能相比，碰后瞬间的总动能为
Object X has mass $2m$ and moves east at speed $v$. Object Y has mass $m$ and moves north at speed $2v$. The magnitudes of the two momentum vectors satisfy物体 X 质量为 $2m$，以速度 $v$ 向东运动；物体 Y 质量为 $m$，以速度 $2v$ 向北运动。两动量向量大小满足
A puck of mass $M$ moves at speed $v$ and undergoes a one-dimensional elastic collision with a stationary puck of mass $3M$. Immediately after the collision, the velocities of the incoming and target pucks are, respectively,质量为 $M$ 的冰球以速度 $v$ 运动，与质量为 $3M$ 的静止冰球发生一维弹性碰撞。碰后瞬间，入射冰球和目标冰球的速度分别为
A $0.020~\mathrm{kg}$ bullet moving horizontally at $300~\mathrm{m/s}$ strikes and embeds itself in a $2.98~\mathrm{kg}$ block hanging at rest at the end of a long string. Take $g = 9.8~\mathrm{m/s^2}$. The maximum height (above the lowest point of the swing) reached by the block-plus-bullet is closest to一颗质量为 $0.020~\mathrm{kg}$ 的子弹以 $300~\mathrm{m/s}$ 水平飞行，嵌入悬挂在长绳末端静止的 $2.98~\mathrm{kg}$ 木块中。取 $g = 9.8~\mathrm{m/s^2}$，木块加子弹摆动到的最大高度（相对摆动最低点）最接近
Two pucks of equal mass $m$ undergo an elastic collision on a frictionless surface. Puck 1 moves east at speed $v$ and strikes puck 2, which is at rest. After the collision, puck 1 moves at $60^\circ$ north of east with speed $v/2$. The speed of puck 2 immediately after the collision is两个质量均为 $m$ 的冰球在无摩擦表面上发生弹性碰撞。冰球 1 以速度 $v$ 向东运动并撞击静止的冰球 2。碰后，冰球 1 以速度 $v/2$ 沿东偏北 $60^\circ$ 方向运动。碰后瞬间冰球 2 的速度大小为
A particle of mass $m$ initially at rest experiences a force $F(t) = \alpha t$ (with $\alpha$ a positive constant) along the $+x$ direction from $t = 0$ to $t = T$. The particle's speed at $t = T$ is质量为 $m$ 的质点由静止开始，在 $t = 0$ 到 $t = T$ 期间受到沿 $+x$ 方向的力 $F(t) = \alpha t$（$\alpha$ 为正常数）。$t = T$ 时质点的速度大小为
A projectile of mass $m$ moving at speed $v$ collides perfectly inelastically with a stationary target of mass $M$. The fraction of the projectile's original kinetic energy that is dissipated (converted to heat, sound, deformation, etc.) is质量为 $m$、速度为 $v$ 的抛射体与质量为 $M$ 的静止靶体发生完全非弹性碰撞。抛射体原有动能中被耗散（转化为热能、声能、形变能等）的比例为
Show all work in the space provided. Partial credit is awarded for correct setup, units, and reasoning. Use $g = 9.8~\mathrm{m/s^2}$ unless otherwise stated.请在给定空间内写出完整解题过程。正确的建立方程、单位和推理均可获得部分得分。除题目另有说明外，取 $g = 9.8~\mathrm{m/s^2}$。
A horizontal force $F(t) = \alpha\,t$, with $\alpha = 24~\mathrm{N/s}$, acts along the $+x$ direction on a $0.50~\mathrm{kg}$ block that is initially at rest on a frictionless surface, from $t = 0$ to $t = 0.50~\mathrm{s}$.水平力 $F(t) = \alpha\,t$（$\alpha = 24~\mathrm{N/s}$）沿 $+x$ 方向作用在初始静止于无摩擦表面上的 $0.50~\mathrm{kg}$ 滑块上，时间从 $t = 0$ 到 $t = 0.50~\mathrm{s}$。
A $60~\mathrm{kg}$ skater holding a $4.0~\mathrm{kg}$ medicine ball stands at rest on frictionless ice. She throws the ball horizontally so that the ball moves at $6.0~\mathrm{m/s}$ relative to the ground.一名持有 $4.0~\mathrm{kg}$ 实心球的 $60~\mathrm{kg}$ 溜冰者静止站在无摩擦冰面上。她水平抛出该球，使其相对地面的速度为 $6.0~\mathrm{m/s}$。
A puck of mass $m_1 = 0.30~\mathrm{kg}$ moves to the right at $v_1 = 4.0~\mathrm{m/s}$ and collides head-on elastically with a puck of mass $m_2 = 0.10~\mathrm{kg}$ moving to the left at $v_2 = 2.0~\mathrm{m/s}$.质量为 $m_1 = 0.30~\mathrm{kg}$ 的冰球以 $v_1 = 4.0~\mathrm{m/s}$ 向右运动，与质量为 $m_2 = 0.10~\mathrm{kg}$、以 $v_2 = 2.0~\mathrm{m/s}$ 向左运动的冰球正面弹性碰撞。
A $2.0~\mathrm{kg}$ puck moving east at $5.0~\mathrm{m/s}$ collides on frictionless ice with a $3.0~\mathrm{kg}$ puck initially at rest. After the collision, the $2.0~\mathrm{kg}$ puck moves at $30^\circ$ north of east with a speed of $2.0~\mathrm{m/s}$.一个 $2.0~\mathrm{kg}$ 的冰球以 $5.0~\mathrm{m/s}$ 向东运动，在无摩擦冰面上与初始静止的 $3.0~\mathrm{kg}$ 冰球碰撞。碰后，$2.0~\mathrm{kg}$ 冰球以 $2.0~\mathrm{m/s}$ 的速度沿东偏北 $30^\circ$ 方向运动。