A piece of wood with mass m = 2.8 kg is held in a vise sandwiched between two wooden jaws as shown in the figure below. A blow from a hammer drives a nail which exerts a force of 440 N on the wood. If the coefficient of static friction between the wood surfaces is 0.66, what minimum normal force must each jaw of the vise exert on the wood block to hold the block in place?
To solve this problem, we need to understand the concept of static friction and its relationship with normal force.
The static friction force, denoted as Fs, can be calculated using the equation Fs = μs * N, where μs is the coefficient of static friction and N is the normal force.
In this case, we need to determine the minimum normal force required to hold the block in place. The maximum static friction force should be equal to the force exerted by the nail, which is 440 N.
So, we can set up the following equation:
Fs = μs * N = 440 N
Now, let's solve for the normal force N.
N = 440 N / μs
Substituting the given coefficient of static friction, μs = 0.66, we have:
N = 440 N / 0.66
N ≈ 666.67 N
Therefore, each jaw of the vise must exert a minimum normal force of approximately 666.67 N to hold the wood block in place.