a body is moving with a velocity v over a rough horizontal surface and comes to rest after traversing a distance s then the co-efficient of friction between body and the surface is
friction work=initial energy= 1/2 m v^2
friction work= mu(mg)*distance
set them equal
distance= 1/2 v^2/(mu*g)
To find the coefficient of friction between the body and the surface, we can start by using the equation of motion for uniformly decelerated motion.
The equation for uniformly decelerated motion is:
v^2 = u^2 - 2as
Where:
- v is the final velocity (in this case, v = 0 because the body comes to rest)
- u is the initial velocity (in this case, u = v because the body was initially at rest)
- a is the acceleration
- s is the distance covered
Since the body comes to rest, v = 0, and the equation reduces to:
0 = v^2 - 2as
0 = 0 - 2as
0 = -2as
Since we are dealing with a rough surface, the force responsible for the deceleration is the force of friction. The force of friction can be expressed as:
F = μN
Where:
- F is the force of friction
- μ is the coefficient of friction
- N is the normal force (which is equal to the weight of the body in this case)
In this scenario, the net force acting on the body in the horizontal direction can be expressed as:
ma = -μmg
Where:
- m is the mass of the body
- g is the acceleration due to gravity
Since we can substitute a = -μg in the equation of motion, we get:
0 = -2s(μg)
0 = -2μsg
Canceling out the zeros, we get:
0 = -2μs
Dividing both sides by -2s, we find:
0/(-2s) = -2μs/(-2s)
0 = μ
Therefore, the coefficient of friction between the body and the rough surface is 0.