Write the energy equation including nonconservative work.

A friction force of \(6\,\mathrm{N}\) acts over \(4\,\mathrm{m}\) opposite the motion. Find its work.

If \(W_{nc}<0\), what happens to mechanical energy?

Why is kinetic friction nonconservative?

A \(2\,\mathrm{kg}\) block moving at \(5\,\mathrm{m\,s^{-1}}\) stops due to friction. Find the work done by friction.

A system has \(K_i+U_i=80\,\mathrm{J}\). Nonconservative work is \(-15\,\mathrm{J}\). Find final mechanical energy.

A block slides \(10\,\mathrm{m}\) with \(f_k=3\,\mathrm{N}\). It starts with \(50\,\mathrm{J}\) of kinetic energy. Find final kinetic energy on level ground.

A motor does \(120\,\mathrm{J}\) of work while friction does \(-35\,\mathrm{J}\). Find the net nonconservative work.

A \(1.0\,\mathrm{kg}\) block slides down a vertical drop of \(2.0\,\mathrm{m}\) and friction does \(-6\,\mathrm{J}\). Starting from rest, find the speed at the bottom.

A \(3\,\mathrm{kg}\) block starts at \(4\,\mathrm{m\,s^{-1}}\) and moves up a rough ramp gaining \(1.0\,\mathrm{m}\) of height. Friction does \(-10\,\mathrm{J}\). Find its final speed.

A block of mass \(m\) starts from rest at height \(h\), slides down a rough track of length \(L\) with constant friction magnitude \(f_k\), then compresses a horizontal spring of constant \(k\) on a rough floor where the same friction magnitude acts. Derive the maximum compression \(x\) and the condition for compression to be possible.

A block starts with speed \(v_0\) and must reach a point height \(h\) above its start. It can take rough path \(1\) of length \(L_1\) or rough path \(2\) of length \(L_2\), with the same constant friction magnitude \(f_k\) on either path. Derive \(v_f^2(L)\), then classify when neither path works, only the shorter path works, or both paths work.