a 2kg mallet is dropped from a height of .6m onto a nail, driving it 3.5 cm into the wood. What is the average force exerted by the mallet on the nail?
thanks
To find the average force exerted by the mallet on the nail, we can use the principle of work and energy. The work done by the mallet is equal to the change in potential energy.
First, let's calculate the potential energy the mallet has when it is at a height of 0.6m. The potential energy is given by the formula:
Potential Energy = mass * gravity * height
mass = 2kg (given)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = 0.6m (given)
Potential Energy = 2kg * 9.8 m/s^2 * 0.6m
Next, let's calculate the work done by the mallet when it drives the nail into the wood. The work is given by the formula:
Work = force * distance
distance = 3.5 cm = 0.035m (given)
force = unknown (what we want to find)
Since the work done is equal to the change in potential energy, we can set up the equation:
Work = Potential Energy
(force * distance) = (mass * gravity * height)
Now, we can solve for the unknown force:
force = (mass * gravity * height) / distance
Substituting the known values:
force = (2kg * 9.8 m/s^2 * 0.6m) / 0.035m
Now we can calculate the force:
force = 33.6 N
Therefore, the average force exerted by the mallet on the nail is 33.6 Newtons.