Two part question

Question

1. The figure shows a claw hammer as it pulls a nail out of a horizontal board. If a force of magnitude 165 N is exerted horizontally as shown, find the force exerted by the hammer claws on the nail. (Assume that the force the hammer exerts on the nail is parallel to the nail). Answer in units of N.
2. Find the force exerted by the surface on the point of contact with the hammer head. Assume that the force the hammer exerts on the nail is parallel to the nail. Answer in units of N.

Answer 1

Treating the point where the hammer touches the table as the fulcrum, and assuming the hammer is not really accelerating much as a result of the forces, we can treat this as a simple static equilibrium problem. The sum of the torques must be zero, or in simpler terms, the torque from the hand on the hammer must be equal and opposite to the torque from the nail.

Therefore, simply set up our equation τ₁=-τ₂

Then replace tau with its Force and Radius representation.

F₁r₁=-F₂r₂

Then simply sub in your values for the forces and the radii from the problem, using the distances from the diagram.

The second part is trickier, but the trick is relatively simple. Instead of torques, we will use forces. Since the upward and downward forces must balance, and the force the person exerts on the claw hammer is completely horizontal, that leaves only the upward normal force from the table balancing with the downward force from the head of the nail on the claw of the hammer.

These two forces must be equal.

If you want a method for solving this problem from the start, simply solve it like any statics problem. Balance the Torques, and balance the forces horizontally and vertically. Then use those simple problems to solve the others if you have too many unknowns, and need to substitute one value into another equation.