physics speed of hanging mass?

Question

The two blocks are connected by a light string that passes over a frictionless pulley with a negligible mass. The 3 kg block lies on a rough horizontal surface with a constant coefficient of kinetic friction 0.3. The hanging block has a mass of 8 kg.The system starts from rest.The acceleration of gravity is 9.8 m/s2 :
What is the speed of the 8 kg hanging mass when it has fallen a height 8 m? Answer in units of m/s.

Answer 1

Force of kinetic friction, f=uR

where u= the coefficient of kinetic friction
R= the normal to the surface

Given: u=0.3
R=3*g

Substitute given values:

f=0.3*3g

Given also: Hanging block of mass 8 kg.

Weight of hanging block, W=8*g

The unbalanced force, F= W-f
=8*g-0.3*3g
=7.1g

F=Ma

Substitute given values for hanging block:

7.1g=8a
a=7.1*9.8/8
=8.70m/s^2

Solve for v using the formula:

v^2-u^2=2as

where v is the final speed, u the initial speed, a the acceleration, and s is the displacement.

Given: u=0
s=8m
and we have solved for a as equal to 8.70m/s^2

Substitute given values, and solve for v:

v^2-0=2*8.70*8
v^2=139.2
v=11.8m/s