(a) -4667 N
First of all, we can calculate the acceleration of the arm and the glove, using the following equation:
[tex]v^2 - u^2 = 2ad[/tex]
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,
[tex]a=\frac{v^2-u^2}{2d}=\frac{0-(10.0 m/s)^2}{2(0.075 m)}=-666.7 m/s^2[/tex]
And since the know the mass of the arm+glove:
m = 7.00 kg
We can now calculate the force exerted:
[tex]F=ma=(7.00 kg)(-666.7 N)=-4,667 N[/tex]
(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
[tex]a=\frac{v^2-u^2}{2d}=\frac{0-(10.0 m/s)^2}{2(0.02 m)}=-2500 m/s^2[/tex]
and so the force is
[tex]F=ma=(7.00 kg)(-2500 m/s^2)=-17,500 N[/tex]
(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:
[tex]W=mg=(476 kg)(9.81 m/s^2)=4670 N[/tex]
Which is quite a lot. Therefore, the force even when gloves are used seems enough to cause damage.
