Spring

A block of mass $m$ on a frictionless incline of angle $\theta$ is connected by a cord that runs over a massless, frictionless pulley to a light spring of spring constant $k$. The block is released from rest when the spring is unstretched.

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 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.

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 block of mass $m$ slides on a horizontal floor with a coefficient of kinetic friction $\mu_k$. It collides head-on with a horizontal spring of spring constant $k$. The block comes to rest after compressing the spring by a distance $x$.

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 $M$ rests on a frictionless horizontal surface. It is connected to a fixed spring of constant $k$. A string attached to this block passes over a frictionless, massless pulley and is connected to a hanging block of mass $2M$. The system is released from rest with the spring in its relaxed (equilibrium) position.

As shown, a block of mass $m$ is on a horizontal surface with a coefficient of kinetic friction $\mu_k$. It is pushed by a compressed spring with spring constant $k$. After leaving the spring (at the spring's equilibrium position), the block slides a distance $d$ before stopping.

A smooth, thin horizontal rod OA can rotate about a vertical axis MN passing through O. Two identical small objects, each with mass $m_1 = m_2 = m$, are threaded onto the rod. They are connected by two identical light springs, each with spring constant $k$ and natural length $L_0$. The first spring connects the axis at O to mass $m_1$, and the second spring connects mass $m_1$ to mass $m_2$.

A spring with a pointer is hung next to a scale marked in millimeters. When a package of weight $W_1 = 110$ N is hung, the pointer indicates $x_1 = 40$ mm. When a package of weight $W_2 = 240$ N is hung, the pointer indicates $x_2 = 60$ mm. A third package of unknown weight $W$ is hung, and the pointer indicates $x_3 = 30$ mm.