Work-Energy

A small ball of mass $m$ is attached to a light string of length $L$. The string's other end is fixed at a pivot point O. The ball is pulled to the side to a point A, where the string is horizontal, and then released from rest. It swings downward in a circular arc.

A car of mass $m$ is traveling on a level road at an initial speed $v_i$. The driver applies the brakes, causing a constant braking force $F_b$. The car's speed reduces to $v_f$ over a distance $d$.

A ball of mass $m$ is thrown vertically downward from a height $h$ with an initial speed $v_i$. It reaches the ground with a final speed $v_f$.

A block is launched up an inclined plane with an initial speed $v_i$. The plane is inclined at an angle $\theta$ to the horizontal, and the coefficient of kinetic friction between the block and the plane is $\mu_k$. The block slides up to a maximum distance and then slides back down to its starting point. Assume the condition for sliding down, $\tan\theta > \mu_k$, is met.

A block of mass $m$ starts from rest at point A, the top of a quarter-circular track of radius $R$. It slides down to point B at the bottom of the track, reaching a final speed $v$.

An object of mass $m$ is thrown vertically upwards with an initial speed $v_0$ from a height $h$ above the ground. The object hits the ground with a final speed $v_f$.

An object of mass $m$ has an initial kinetic energy $K$. It moves up an inclined plane with an angle of inclination $\theta$.

Water is lifted at a constant speed from a well of depth $H = 10$ m. The combined mass of the bucket and water is $M = 20$ kg. The rope has a linear mass density of $\lambda = 200$ g/m.

An ice block floating in a river is pushed through a displacement $\vec{d} = (15 \text{ m})\hat{i} - (12 \text{ m})\hat{j}$ along a straight embankment by rushing water, which exerts a force $\vec{F} = (210 \text{ N})\hat{i} - (150 \text{ N})\hat{j}$ on the block.

A block is sent up a frictionless ramp along which an x axis extends upward. Figure below gives the kinetic energy of the block as a function of position x; the scale of the figure's vertical axis is set by $K_s = 40.0$ J. If the block's initial speed is 4.00 m/s, what is the normal force on the block?