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=10m/s^2)
a body 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=10m/s)
A body of mass 25kg moving at 3m/s on a rough horizontal floor is brought to rest after sliding through a distance of 2.50m on d floor.calculate the coefficient of sliding friction
To calculate the coefficient of sliding friction, we need to use the equation for friction:
Frictional force (Ff) = coefficient of sliding friction (μ) x Normal force (Fn)
The normal force is the force exerted by the floor on the body, which is equal to the weight of the body. We can calculate the weight using the formula:
Weight (W) = mass (m) x acceleration due to gravity (g)
Given:
Mass (m) = 25 kg
Acceleration due to gravity (g) = 10 m/s^2
Weight (W) = (25 kg) x (10 m/s^2) = 250 N
Now, to calculate the frictional force, we can use Newton's second law of motion:
Frictional force (Ff) = mass (m) x acceleration (a)
Since the body is brought to rest, the final velocity is 0 m/s, and the initial velocity is 3 m/s. The distance traveled (s) is given as 2.5 m. We can use the equation:
Final velocity (v)² = Initial velocity (u)² + 2 x acceleration (a) x distance (s)
0² = 3² + 2 x a x 2.5
0 = 9 + 5a
5a = -9
a = -1.8 m/s² (the negative sign indicates deceleration)
The frictional force is equal to the mass times the acceleration:
Frictional force (Ff) = (25 kg) x (-1.8 m/s²) = -45 N
Since friction opposes motion, the frictional force is in the opposite direction to the initial velocity.
Now, we can calculate the coefficient of sliding friction (μ) using the formula:
μ = Frictional force (Ff) / Normal force (Fn)
μ = -45 N / 250 N = -0.18
The coefficient of sliding friction is -0.18. Note that the negative sign indicates that the force of friction is acting opposite to the direction of motion.