A body of mass 25kg moving at 3m/s on rough horizontal floor is brought to rest after shifting through a distance of 2.5m on the floor. calculate the coefficient of sliding friction
F = - mu m g = m a
so what is a?
average speed = (3+0)/2 = 1.5 m/s
so t = 2.5 meters / 1.5 m/s = 1.67 seconds
v = Vi + a t
0 = 3 + 1.67 a
a = -1.8 m/s^2
back to
-mu m g = m a
mu = a/g = 1.8/g = 0.183
To calculate the coefficient of sliding friction, we can use the formula:
Frictional Force = μ * Normal Force
Here, the normal force is equal to the weight of the body, which can be calculated by multiplying the mass (m) with the acceleration due to gravity (g).
Normal Force = m * g
Given:
- Mass (m) = 25 kg
- Initial velocity (u) = 3 m/s
- Final velocity (v) = 0 m/s
- Distance (d) = 2.5 m
First, let's calculate the acceleration (a) using the equation:
v^2 = u^2 + 2ad
0 = (3 m/s)^2 + 2*a*2.5 m
0 = 9 m^2/s^2 + 5a
-9 m^2/s^2 = 5a
a = -9 m^2/s^2 / 5
Now, let's calculate the frictional force (N) using Newton's second law:
Frictional Force = mass * acceleration
Frictional Force = 25 kg * (-9 m^2/s^2 / 5)
Next, substitute the frictional force into the first equation to find the coefficient of sliding friction (μ):
Frictional Force = μ * Normal Force
μ * Normal Force = 25 kg * (-9 m^2/s^2 / 5)
Finally, calculate the normal force (N) using the formula:
Normal Force = mass * acceleration due to gravity
Normal Force = 25 kg * 9.8 m/s^2
Substituting the values, we can solve for the coefficient of sliding friction (μ).
To calculate the coefficient of sliding friction, we need to use the equation of motion for a body undergoing constant retardation.
The equation is: v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the body is brought to rest)
u = initial velocity (3 m/s)
a = acceleration (retardation due to friction)
s = distance (2.5 m)
Since the body is brought to rest, the final velocity (v) is 0 m/s.
Plugging in the values into the equation, we get:
0^2 = 3^2 + 2a(2.5)
0 = 9 + 5a
Rearranging the equation, we have:
5a = -9
Dividing both sides by 5:
a = -9/5
Now, we need to calculate the coefficient of sliding friction (μ). The equation to calculate μ is:
μ = a/g
Where g is the acceleration due to gravity (9.8 m/s^2).
Substituting the value of a, we get:
μ = (-9/5) / 9.8
Now, calculating the value of μ:
μ = -1.8 / 9.8
μ ≈ -0.1837
The coefficient of sliding friction is approximately -0.1837. Note that the coefficient of friction can be positive or negative, indicating the direction of the friction force. In this case, the negative sign indicates that the friction force opposes the motion.