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 concept of work and energy.
First, let's calculate the potential energy of the mallet before it is dropped. The potential energy (PE) is given by the formula:
PE = m * g * h
Where:
m = mass of the mallet = 2 kg
g = acceleration due to gravity = 9.8 m/s²
h = height from which the mallet is dropped = 0.6 m
Substituting the given values, we get:
PE = 2 kg * 9.8 m/s² * 0.6 m
PE = 11.76 J
Now, when the mallet falls and drives the nail into the wood, the potential energy is converted into work done on the nail. The work done (W) is given by:
W = F * d
Where:
F = force exerted by the mallet on the nail
d = distance the nail is driven into the wood = 3.5 cm = 0.035 m
Substituting the known values, we get:
11.76 J = F * 0.035 m
Rearranging the equation to solve for F, we have:
F = 11.76 J / 0.035 m
F = 335.31 N
Therefore, the average force exerted by the mallet on the nail is approximately 335.31 Newtons.