質點運動學與力學能量守恆定律

📝 歷屆考古題

• 115年 hce_nchu 第3題
  Two objects, A and B, have a mass ratio of $m_A : m_B = 2 : 1$. If both objects have the same kineti…
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• 115年 hce_nchu 第10題
  Two satellites, A and B, orbit the Earth in uniform circular motion. If the orbital radius of satell…
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• 115年 hce_nchu 第15題
  A $2\text{ kg}$ object is launched from the ground with an initial speed of $30\text{ m/s}$ at an an…
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• 115年 hce_nchu 第17題
  A uniform rope of length $L$ and mass $M$ lies on a frictionless horizontal table. If a horizontal f…
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• 115年 hce_nchu 第20題
  A force $F = (3x^2 + 2x)\text{ N}$ (where $x$ is in meters) acts on an object along the $x$-axis. As…
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• 115年 hce_nchu 第32題
  A long ladder leans against a smooth vertical wall, with its base resting on a rough horizontal floo…
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• 115年 hce_nchu 第48題
  A bullet of mass $m$ is fired horizontally with a speed $v$ into a stationary wooden block of mass $M$…
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• 114年 hce_nchu 第1題
  The graph shows acceleration versus time for three different objects, $\alpha$, $\beta$, and $\gamma$…
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• 114年 hce_nchu 第2題
  Consider a projectile launched upward near the surface of Earth from the origin at some angle $\theta_0$…
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• 114年 hce_nchu 第3題
  A 740-kg elevator accelerates upward at $0.2 \text{ m/s}^2$, pulled by a cable of negligible mass. N…
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• 114年 hce_nchu 第4題
  Blocks of 1, 2, and 3 kg are lined up on a frictionless table, as shown in the figure, with a 12-N f…
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• 114年 hce_nchu 第5題
  Patients with severe leg breaks are often placed in traction, with an external force countering musc…
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• 114年 hce_nchu 第6題
  An elastic cord used in bungee jumping is normally 10 m long and has spring constant $k = 250 \text{ N/m}$…
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• 114年 hce_nchu 第7題
  A 1.5-tonne car accelerates from 10 to 20 m/s in 10 s on a flat road. How much work is done on the c…
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• 114年 hce_nchu 第8題
  Based on Newton's law of universal gravitation and Newton's second law of motion, Kepler's third law…
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• 114年 hce_nchu 第9題
  A rocket is launched vertically upward at velocity $v$ around the surface of Earth. The constant of…
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• 114年 hce_nchu 第10題
  In the figure, blocks $B$ and $C$ have masses $2m$ and $m$, respectively, and are at rest on a frict…
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• 114年 hce_nchu 第11題
  A uniform, narrow rod of mass $M$ and length $L$ rotates freely about an axis through one of its end…
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• 114年 hce_nchu 第12題
  A solid ball of mass $M$ and radius $R$ starts from rest and rolls down a hill. Its center of mass d…
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• 114年 hce_nchu 第13題
  For a simple pendulum with length $L$ swinging back and forth through a small angle, under the influ…
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• 114年 hce_nchu 第14題
  The figure shows three pairs of forces acting on an object. Which pair, acting as the only forces on…
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• 113年 hce_nchu 第1題
  Cart A, of mass $m$, starts from rest and travels in a straight line with acceleration $a$. It trave…
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• 113年 hce_nchu 第2題
  An automobile traveling along a straight road increases its speed from $30.0 \text{ m/s}$ to $50.0 \text{ m/s}$…
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• 113年 hce_nchu 第3題
  A particle moves in the $xy$ plane with a constant acceleration given by $\vec{a} = -4\hat{j} \text{ m/s}^2$…
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• 113年 hce_nchu 第4題
  Two balls, projected at different times so they don't collide, have trajectories A and B, as shown b…
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• 113年 hce_nchu 第5題
  If $M = 6.0 \text{ kg}$, what is the tension in string 2? Note that the acceleration due to gravity…
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• 113年 hce_nchu 第6題
  The horizontal surface on which the objects slide is frictionless. If M = $1.0 \text{ kg}$ and the m…
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• 113年 hce_nchu 第7題
  The total force needed to drag a box at constant speed across a surface with coefficient of kinetic…
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• 113年 hce_nchu 第8題
  A race car traveling at $100 \text{ m/s}$ enters an unbanked turn of $400 \text{ m}$ radius. The coe…
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• 113年 hce_nchu 第9題
  A certain pendulum consists of a $1.5\text{-kg}$ mass swinging at the end of a string (length = $2.0 \text{ m}$…
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• 113年 hce_nchu 第10題
  Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mas…
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• 113年 hce_nchu 第11題
  A ball of mass $m_B$ is released from rest and acquires velocity of magnitude $v_B$ before hitting t…
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• 113年 hce_nchu 第12題
  A wheel rotating about a fixed axis with a constant angular acceleration of $2.0 \text{ rad/s}^2$ tu…
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• 113年 hce_nchu 第13題
  A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel…
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• 113年 hce_nchu 第14題
  A body of mass $5.0 \text{ kg}$ is suspended by a spring which stretches $10 \text{ cm}$ when the ma…
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• 113年 hce_nchu 第15題
  The motion of a particle connected to a spring is described by $x = 10 \sin \pi t$. At what time (in…
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• 112年 hce_nchu 第1題
  Dagwood and Blondie are driving two identical cars. Blondie is passing Dagwood at twice his speed. T…
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• 112年 hce_nchu 第2題
  On a distant planet where the gravitational constant $g = 6.0 \text{ m/s}^2$, Sherlock Holmes droppe…
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• 112年 hce_nchu 第3題
  Two blocks are in contact on a frictionless table. A horizontal force is applied to one block as sho…
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• 112年 hce_nchu 第4題
  The accelerations of the blocks A and B respectively as seen in the situation shown in the figure ar…
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• 112年 hce_nchu 第5題
  For the conical pendulum shown, the $0.40 \text{ kg}$ mass has a periodic time of $1.90 \text{ s}$.…
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• 112年 hce_nchu 第6題
  An astronaut, spaced out as usual, sits in her room at position "F" on the outer rim of a wheel-shap…
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• 112年 hce_nchu 第7題
  A piece of thin uniform wire of mass $m$ and length $3b$ is bent into an equilateral triangle. Find…
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• 112年 hce_nchu 第8題
  A uniform solid sphere of mass $M$ and radius $R$ rotates with an angular speed $\omega$ about an ax…
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• 112年 hce_nchu 第9題
  A record is dropped vertically onto a freely rotating (undriven) turntable. Frictional forces act to…
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• 112年 hce_nchu 第10題
  In the figure, a mass of $31.77 \text{ kg}$ is attached to a light string that is wrapped around a c…
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• 112年 hce_nchu 第11題
  A uniform sign is supported against a wall at point $P$ as shown in the figure. If the sign is a squ…
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• 112年 hce_nchu 第12題
  A $2.0 \text{ kg}$ block on a frictionless table is connected to two ideal massless springs with spr…
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• 112年 hce_nchu 第13題
  In the figure, two masses, $M = 16 \text{ kg}$ and $m = 12.8 \text{ kg}$, are connected to a very li…
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• 112年 hce_nchu 第24題
  A crane lifts a $425 \text{ kg}$ steel beam vertically a distance of $117 \text{m}$. How much work d…
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• 112年 hce_nchu 第25題
  A certain spherical asteroid has a mass of $3.5 \times 10^{16} \text{ kg}$ and a radius of $8.8 \text{ km}$…
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• 111年 hce_nchu 第1題
  An object starts from rest at the origin and moves along the x axis with a constant acceleration of…
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• 111年 hce_nchu 第2題
  A ball is thrown horizontally from the top of a $20\text{-m}$ high hill. It strikes the ground at an…
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• 111年 hce_nchu 第3題
  The speed of a particle moving in a circle $2.0\text{ m}$ in radius increases at the constant rate o…
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• 111年 hce_nchu 第4題
  Block A, with a mass of $10\text{ kg}$, rests on a $30^\circ$ incline. The coefficient of kinetic fr…
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• 111年 hce_nchu 第5題
  Block A, with mass $m_A$, is initially at rest on a horizontal floor. Block B, with mass $m_B$, is i…
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• 111年 hce_nchu 第6題
  As a $2.0\text{-kg}$ object moves from $(2\hat{i}+5\hat{j})\text{ m}$ to $(6\hat{i}-2\hat{j})\text{ m}$…
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• 111年 hce_nchu 第7題
  A certain pendulum consists of a $1.5\text{-kg}$ mass swinging at the end of a string (length = $2.0\text{ m}$…
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• 111年 hce_nchu 第8題
  A $10\text{-g}$ bullet moving horizontally with a speed of $2.0\text{ km/s}$ strikes and passes thro…
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• 111年 hce_nchu 第9題
  A wheel of radius $R$ is mounted on a frictionless, horizontal axle that is perpendicular to the whe…
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• 111年 hce_nchu 第10題
  A merry-go-round of radius $R = 2.0\text{ m}$ has a moment of inertia $I = 250\text{ kg}\cdot\text{m}^2$…
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• 111年 hce_nchu 第11題
  The figure shows a uniform rod (length $L = 1.0\text{ m}$, mass $m = 2.0\text{ kg}$) suspended from…
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• 111年 hce_nchu 第12題
  A ball of mass $m_B$ is released from rest and acquires velocity of magnitude $v_B$ before hitting t…
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• 111年 hce_nchu 第13題
  An asteroid revolves around the Sun with a perihelion $0.5\text{ AU}$ and an aphelion of $7.5\text{ AU}$…
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• 111年 hce_nchu 第14題
  A $3.0\text{-kg}$ block is on a horizontal surface. The block is at rest when, at $t = 0$, a force (…
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• 111年 hce_nchu 第15題
  Star X is 200 light-years away from the Earth. Astronauts Joe and Mary, both at age of 30, travel to…
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• 111年 hce_nchu 第18題
  A $5.23\text{-g}$ pebble is dropped from a $300\text{-m}$ building. If it reaches a terminal velocit…
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• 111年 hce_nchu 第23題
  A police crime lab is trying to determine whether someone was murdered or died as a result of an acc…
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