a body of mass 25kg,moving at 3m/s on a rough horizontal floor is brought to rest after sliding through a distance of 2.5m on the floor. calculate the coefficient of sliding friction [g=10ms-2]
To calculate the coefficient of sliding friction, we can use the equation:
Frictional force = coefficient of sliding friction * Normal force
First, we need to find the frictional force. The work done by frictional force can be given by:
Work = Frictional force * Distance
Since the body comes to rest, the work done by frictional force is equal to the initial kinetic energy. Therefore:
Frictional force * Distance = (1/2) * mass * velocity^2
Frictional force = (1/2) * mass * velocity^2 / Distance
Frictional force = (1/2) * 25kg * (3m/s)^2 / 2.5m
Frictional force = 22.5 N
Now, we need to find the normal force acting on the body. The normal force is equal to the weight of the body, which is given by:
Weight = mass * gravity
Weight = 25kg * 10 m/s^2
Weight = 250 N
Since the body is on a horizontal floor, the normal force is equal to the weight of the body:
Normal force = 250 N
Now, we can calculate the coefficient of sliding friction using the equation:
Frictional force = coefficient of sliding friction * Normal force
22.5 N = coefficient of sliding friction * 250 N
Coefficient of sliding friction = 22.5 N / 250 N
Coefficient of sliding friction = 0.09
Therefore, the coefficient of sliding friction is 0.09.
To calculate the coefficient of sliding friction, we need to use the following equation:
Frictional force (F) = coefficient of sliding friction (μ) × Normal force (N)
First, let's find the normal force acting on the body. The normal force is the force exerted by a surface to support the weight of an object resting on it.
Since the body is initially moving horizontally at a constant velocity, the normal force is equal in magnitude and opposite in direction to the gravitational force acting on the body.
Normal force (N) = mass (m) × gravitational acceleration (g)
Given that the mass (m) is 25 kg and the gravitational acceleration (g) is 10 m/s^2:
N = 25 kg × 10 m/s^2
N = 250 N
Now, let's calculate the frictional force (F). The frictional force can be found using the equation:
F = mass (m) × acceleration due to sliding (a)
The acceleration due to sliding can be determined using the following equation:
a = Change in velocity (Δv) / Time taken (t)
The body is brought to rest, so the final velocity (vf) is 0 m/s. The initial velocity (vi) is 3 m/s. Thus, the change in velocity (Δv) is:
Δv = vf - vi
Δv = 0 m/s - 3 m/s
Δv = -3 m/s (negative sign indicates direction opposite to motion)
We are not given the time taken (t) directly, so we can use the equation of motion:
Δx = (vi + vf) / 2 × t
Rearranging this equation to solve for time:
t = 2 × Δx / (vi + vf)
t = 2 × 2.5 m / (3 m/s + 0 m/s)
t = 5 m / 3 m/s
t = 1.67 s
Now we can find the acceleration (a) using:
a = Δv / t
a = -3 m/s / 1.67 s
a ≈ -1.80 m/s^2 (rounded to two decimal places)
Finally, let's calculate the frictional force (F) using:
F = m × a
F = 25 kg × -1.80 m/s^2
F = -45 N (negative sign indicates opposite direction to motion)
Substituting the known values into the equation for frictional force:
-45 N = μ × 250 N
To find μ, divide both sides of the equation by 250 N:
- 45 N / 250 N = μ × 250 N / 250 N
- 0.18 = μ
So, the coefficient of sliding friction (μ) is approximately 0.18.