AP-Style Practice QuestionsAP 风格练习题
Topics主题 3.1 - 3.5MECH
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.在草稿纸上写出所有辅助步骤。每题均标注了对应的力学主题，以及该 AP 考试部分是否允许使用计算器。除非题目另有说明，取 $g = 9.8~\mathrm{m/s^2}$。
A $2.0~\mathrm{kg}$ block moves at $6.0~\mathrm{m/s}$. Its kinetic energy is一个质量为 $2.0~\mathrm{kg}$ 的滑块以 $6.0~\mathrm{m/s}$ 的速度运动，其动能为
A constant force of magnitude $F = 50~\mathrm{N}$ pulls a block through a displacement of $d = 4.0~\mathrm{m}$. The angle between the force and the displacement is $60^\circ$. The work done by the force is一个大小为 $F = 50~\mathrm{N}$ 的恒力拉动滑块位移 $d = 4.0~\mathrm{m}$，力与位移之间的夹角为 $60^\circ$，该力做的功为
A motor performs $600~\mathrm{J}$ of work over $30~\mathrm{s}$. Its average power output is一台电动机在 $30~\mathrm{s}$ 内做了 $600~\mathrm{J}$ 的功，其平均功率为
A spring with $k = 200~\mathrm{N/m}$ is compressed $0.10~\mathrm{m}$ from its natural length. The elastic potential energy stored in the spring is一根弹簧的弹簧常数 $k = 200~\mathrm{N/m}$，从自然长度压缩 $0.10~\mathrm{m}$，弹簧中储存的弹性势能为
A $5.0~\mathrm{kg}$ block moving at $10~\mathrm{m/s}$ along a horizontal surface is brought to rest by friction alone. The total work done on the block by friction is一个质量为 $5.0~\mathrm{kg}$ 的滑块以 $10~\mathrm{m/s}$ 沿水平面运动，仅由摩擦力使其静止，摩擦力对滑块做的总功为
A particle moves along the $x$-axis under a conservative potential $U(x) = 3x^2 - 6x + 2$ (J, with $x$ in m). The force on the particle at $x = 1~\mathrm{m}$ is一个质点在保守势能 $U(x) = 3x^2 - 6x + 2$（J，$x$ 单位为 m）的作用下沿 $x$ 轴运动，质点在 $x = 1~\mathrm{m}$ 处所受的力为
A $1.0~\mathrm{kg}$ block is released from rest on a frictionless ramp at height $h = 5.0~\mathrm{m}$ above the bottom. Take $g = 10~\mathrm{m/s^2}$. Its speed at the bottom of the ramp is一个质量为 $1.0~\mathrm{kg}$ 的滑块从无摩擦斜面上距底部高度 $h = 5.0~\mathrm{m}$ 处由静止释放，取 $g = 10~\mathrm{m/s^2}$，到达斜面底部时的速度为
A force $F(x) = 3x^2 + 2x$ (in N, with $x$ in m) acts on a particle as it moves along the $x$-axis. The work done by this force as the particle moves from $x = 0$ to $x = 2~\mathrm{m}$ is一个力 $F(x) = 3x^2 + 2x$（N，$x$ 单位为 m）作用于质点沿 $x$ 轴运动，质点从 $x = 0$ 运动到 $x = 2~\mathrm{m}$ 过程中该力做的功为
A particle moves under the potential $U(x) = x^3 - 3x$ (J, with $x$ in m). Which statement about its equilibria is correct?一个质点在势能 $U(x) = x^3 - 3x$（J，$x$ 单位为 m）的作用下运动，关于其平衡位置，下列说法正确的是
A spring with $k = 200~\mathrm{N/m}$ is compressed by $0.30~\mathrm{m}$ and used to launch a $0.50~\mathrm{kg}$ block on a frictionless surface. The block's speed after release is弹簧常数 $k = 200~\mathrm{N/m}$ 的弹簧被压缩 $0.30~\mathrm{m}$，在无摩擦面上弹射一个质量为 $0.50~\mathrm{kg}$ 的滑块，释放后滑块的速度为
A $1500~\mathrm{kg}$ car climbs a $5^\circ$ incline at constant velocity $v = 20~\mathrm{m/s}$. Drag is negligible. The instantaneous mechanical power delivered by the engine is closest to一辆质量为 $1500~\mathrm{kg}$ 的汽车以匀速 $v = 20~\mathrm{m/s}$ 爬上 $5^\circ$ 的坡道，空气阻力不计，发动机输出的瞬时机械功率最接近
Which of the following forces is not conservative?下列哪个力不是保守力？
A car's speed is doubled. Its kinetic energy一辆汽车的速度翻倍，其动能
A particle moves along the straight line from $(0, 0)$ to $(2, 3)$ (in metres) under the force $\vec F = 2y\,\hat\imath + 3x\,\hat\jmath$ (in N). The work done by $\vec F$ along this path is一个质点在力 $\vec F = 2y\,\hat\imath + 3x\,\hat\jmath$（N）的作用下沿直线从 $(0, 0)$ 运动到 $(2, 3)$（单位：m），$\vec F$ 沿该路径所做的功为
A particle moves along the $x$-axis under the potential $U(x) = x^3 - 9x$ (J, with $x$ in m). The locations of the particle's stable equilibrium are一个质点在势能 $U(x) = x^3 - 9x$（J，$x$ 单位为 m）的作用下沿 $x$ 轴运动，质点稳定平衡的位置为
A car of mass $m$ starts from rest on a flat road and is driven by an engine that delivers constant mechanical power $P$. Drag is neglected. The car's speed at time $t$ is一辆质量为 $m$ 的汽车从静止出发在平路上行驶，发动机以恒定机械功率 $P$ 驱动，忽略阻力，汽车在时刻 $t$ 的速度为
A small block is released from rest at height $h$ on a frictionless track that leads into a vertical loop of radius $R$. The minimum value of $h$ such that the block maintains contact with the track at the top of the loop is一个小滑块从无摩擦轨道上高度 $h$ 处由静止释放，进入半径为 $R$ 的竖直圆环，使滑块在圆环顶端保持与轨道接触所需 $h$ 的最小值为
A pump lifts water from a well of depth $h = 30~\mathrm{m}$ and delivers it to ground level at a steady rate of $5.0~\mathrm{kg/s}$. Assuming the water is delivered with negligible exit speed, the minimum mechanical power the pump must supply is closest to一台水泵以 $5.0~\mathrm{kg/s}$ 的稳定速率将水从深度 $h = 30~\mathrm{m}$ 的水井中提升至地面，假设出水口速度可忽略不计，水泵需提供的最小机械功率最接近
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.在所提供的空白处写出所有解题过程。正确的建立方程、单位和推理均可获得部分分数。除非另有说明，使用 $g = 9.8~\mathrm{m/s^2}$。
A $0.50~\mathrm{kg}$ block is released from rest on a frictionless curved ramp at height $h = 1.2~\mathrm{m}$ above a horizontal floor. After leaving the ramp it slides along the floor and compresses a spring of constant $k = 600~\mathrm{N/m}$ until it momentarily stops. After the spring releases the block, the block slides back across the same horizontal floor, but on the return trip the floor has kinetic-friction coefficient $\mu_k = 0.20$.一个质量为 $0.50~\mathrm{kg}$ 的滑块从无摩擦弧形斜面上距水平地面高度 $h = 1.2~\mathrm{m}$ 处由静止释放，离开斜面后沿地面滑动，压缩弹簧常数 $k = 600~\mathrm{N/m}$ 的弹簧直至瞬间停止。弹簧将滑块弹回后，滑块沿同一水平地面滑回，但返回途中地面的动摩擦系数 $\mu_k = 0.20$。
A particle of mass $m = 2.0~\mathrm{kg}$ moves along the $x$-axis under the conservative potential $U(x) = \tfrac{1}{4}x^4 - 2x^2 + 3$ (J, with $x$ in m).一个质量为 $m = 2.0~\mathrm{kg}$ 的质点在保守势能 $U(x) = \tfrac{1}{4}x^4 - 2x^2 + 3$（J，$x$ 单位为 m）的作用下沿 $x$ 轴运动。
A $4.0~\mathrm{kg}$ block slides along a horizontal surface whose kinetic-friction coefficient varies with position: $\mu_k(x) = 0.10 + 0.05\,x$, where $x$ is in metres. The block enters $x = 0$ moving with speed $v_0 = 5.0~\mathrm{m/s}$.一个质量为 $4.0~\mathrm{kg}$ 的滑块沿水平面滑动，该面的动摩擦系数随位置变化：$\mu_k(x) = 0.10 + 0.05\,x$，其中 $x$ 单位为 m。滑块以速度 $v_0 = 5.0~\mathrm{m/s}$ 从 $x = 0$ 处进入。
A car of mass $m = 1200~\mathrm{kg}$ starts from rest on a flat, straight road. Its engine delivers constant mechanical power $P = 60~\mathrm{kW}$ from $t = 0$ onward. Drag and rolling resistance are neglected.一辆质量为 $m = 1200~\mathrm{kg}$ 的汽车从静止出发沿平直道路行驶，发动机从 $t = 0$ 起以恒定机械功率 $P = 60~\mathrm{kW}$ 驱动，忽略空气阻力和滚动阻力。