(a) -4667 N
First of all, we can calculate the acceleration of the arm and the glove, using the following equation:
where
v = 0 is the final speed
u = 10 m/s is the initial speed
a is the acceleration
d = 7.50 cm = 0.075 m is the distance through which the arm and the glove move before coming to a stop
Solving for a,
And since the know the mass of the arm+glove:
m = 7.00 kg
We can now calculate the force exerted:
(b) -17500 N
We can repeat the problem, but this time the stopping distance is different:
d = 2.00 cm = 0.02 m
So the acceleration is
and so the force is
(c) Yes
The force exerted when the glove is used is
F = 4667 N
We see that this force corresponds approximately to the weight of an object of mass m=476 kg, in fact:
Which is quite a lot. Therefore, the force even when gloves are used seems enough to cause damage.