A box of mass $50 \mathrm{kg}$ is at rest on a slope, which is at an angle of $26°$ to the horizontal. The coefficient of friction is $0.4.$ The box is held in place by a rope attached to a winch pulling up the slope and parallel to it. Find the minimum and maximum possible values for the tension, $T,$ which the winch could provide for the box to remain in equilibrium.

A car of mass $1350 \mathrm{kg}$ is at rest on a rough slope at an angle of $7°$ to the horizontal. A man tries to push it down the slope, exerting a force of $500 \mathrm{N},$ but cannot get it to move.

Find the angle that the total contact force makes with the slope.

A car of mass $1350 \mathrm{kg}$ is at rest on a rough slope at an angle of $7°$ to the horizontal. A man tries to push it down the slope, exerting a force of $500 \mathrm{N},$ but cannot get it to move.

When the man stops pushing, the car remains in equilibrium. Find the angle that the total contact force makes with the slope.

A ring of mass $2 \mathrm{kg}$ is held in place at rest on a rough horizontal wire. It is attached to a string that is at an angle of $40°$ above the horizontal.

Explain why once the ring is released it can never be in equilibrium, however high the coefficient of friction, when the tension in the string satisfies $T\sin 40=2\mathrm{g}.$

A ring of mass $2 \mathrm{kg}$ is held in place at rest on a rough horizontal wire. It is attached to a string that is at an angle of $40°$ above the horizontal.

Show that when the tension is $100 \mathrm{N}$ the coefficient of friction must be at least $1.73$ for the ring to be in equilibrium, but when the tension increases to $200 \mathrm{N}$ the coefficient of friction can be as low as $1.41$ with the ring remaining in equilibrium. Explain why.

A box of mass $14 \mathrm{kg}$ is on horizontal ground. It is dragged by a horizontal force of $21 \mathrm{N}.$ The surface is rough and the coefficient of friction between the surface and the box is $0.1.$

Resolve vertically to find the size of the normal contact force.

A box of mass $14 \mathrm{kg}$ is on horizontal ground. It is dragged by a horizontal force of $21 \mathrm{N}.$ The surface is rough and the coefficient of friction between the surface and the box is $0.1.$

Find the size of the frictional force.

A box of mass $14 \mathrm{kg}$ is on horizontal ground. It is dragged by a horizontal force of $21 \mathrm{N}.$ The surface is rough and the coefficient of friction between the surface and the box is $0.1.$

Find the acceleration of the box.