A hammer is being used to pull a nail out of a horizontal board. L = 32 cm and d = 5.2 cm. If a force of 158 N is exerted horizontally as shown, calculate the force (in N) exerted by the hammer claws on the nail.
To calculate the force exerted by the hammer claws on the nail, we need to consider the principles of torque and equilibrium.
First, let's define the variables:
L = length of the lever arm (32 cm or 0.32 m)
d = perpendicular distance from the nail to the line of action of the force (5.2 cm or 0.052 m)
F = force exerted horizontally (158 N)
Torque is a measure of the turning force around a pivot point. It is calculated by multiplying the force applied by the perpendicular distance from the pivot point to the line of action of the force.
The torque exerted by the force (T) is given by the formula:
T = F * d
In this case, the torque exerted by the force is equal to the torque exerted by the hammer claws on the nail. To calculate the force exerted by the hammer claws (F_nail), we rearrange the formula:
F_nail = T / d
Substituting the values we have:
T = 158 N * 0.052 m
T = 8.216 Nm
Finally, we can calculate the force exerted by the hammer claws on the nail:
F_nail = 8.216 Nm / 0.032 m
F_nail ≈ 252.33 N
Therefore, the force exerted by the hammer claws on the nail is approximately 252.33 N.