A body of mass 25kg, moving at 3ms-1 on a rough horizontal floor is at rest after sliding through a distance of 2.50m on the floor. Calculate the co-efficie...
A body of mass 25kg, moving at 3ms-1 on a rough horizontal floor is at rest after sliding through a distance of 2.50m on the floor. Calculate the co-efficient of sliding friction. [g = 10.0ms-2]
Answer Details
To calculate the coefficient of sliding friction, we need to use the equation:
frictional force = coefficient of sliding friction x normal force
First, let's calculate the initial kinetic energy of the body:
Kinetic energy = 0.5 x mass x velocity^2
= 0.5 x 25 x (3)^2
= 112.5 J
Next, we need to calculate the work done by the frictional force, which is equal to the initial kinetic energy minus the final kinetic energy (since the body comes to rest):
Work done by friction = initial kinetic energy - final kinetic energy
= 112.5 - 0
= 112.5 J
Now, let's calculate the frictional force:
Frictional force = work done by friction / distance
= 112.5 / 2.50
= 45 N
Finally, we can calculate the coefficient of sliding friction:
Coefficient of sliding friction = frictional force / normal force
To find the normal force, we can use Newton's second law of motion:
Sum of forces = mass x acceleration
Since the body is at rest, the acceleration is 0, and the sum of forces is equal to the weight of the body:
Sum of forces = weight = mass x gravity
= 25 x 10
= 250 N
Therefore, the normal force is 250 N.
Now we can calculate the coefficient of sliding friction:
Coefficient of sliding friction = frictional force / normal force
= 45 / 250
= 0.18
Therefore, the coefficient of sliding friction is 0.18.
Answer: The coefficient of sliding friction is 0.18.