Mechanical Energy And Conservation

A light spring with a spring constant $k = 360$ N/m has one end fixed. The other end is attached to a small ball of mass $m = 100$ g, which is placed on a smooth horizontal surface. The ball is pulled from its equilibrium position to a displacement of $x_1 = 10$ cm and then released from rest.

A 2.0 kg block on a horizontal surface is pushed against a light horizontal spring (spring constant 200 N/m), compressing it by 15 cm. The block is then released from rest. After leaving the spring (at its equilibrium position), the block slides 60 cm before coming to a stop.

A 10 kg projectile is fired with an initial speed of 500 m/s.

A spring in a spring gun has a spring constant $k = 80$ N/m. The trigger holds the spring compressed by 5 cm. A 10 g bullet is placed in the barrel against the spring. The barrel is horizontal.

A ball of mass $m$ is attached to a string of length $L$. The other end of the string is fixed. The ball is released from rest with the string held in a horizontal position. A fixed peg is located at point $P$, a vertical distance $d$ below the fixed end. When the ball swings down, the string catches on the peg, and the ball continues its swing about the peg.

A 2.0 kg block is dropped from a height of 0.40 m onto a vertical spring standing on the ground. The spring has a spring constant $k = 2000$ N/m.

A projectile is launched with an initial speed $v_0$.

An object is attached to a vertical spring. When lowered slowly, it reaches an equilibrium position where the spring is extended by a length $d$.

A 5.0 g bullet is fired vertically upward by a spring gun. The spring must be compressed by at least 10 cm for the bullet to reach a target 20 m high (measured from the muzzle).

A block of mass $m$ is pushed against a horizontal spring of spring constant $k$, compressing it by a distance $x$. The block is initially at rest on a frictionless surface. The block is then released and slides away from the spring. It leaves the spring at the spring's relaxed length and then travels over a rough horizontal floor with a coefficient of kinetic friction $\mu_k$. The block comes to a stop after traveling a distance $D$ on the rough surface.