A body of mass 25km moving a 3.0ms on a rough horizotal floor is brought to rest after slinding through a distance of 2.5m on the floor. Calculate the coefficient of static friction (g=10m/s)
To calculate the coefficient of static friction, we need to use the equation for friction:
F_friction = μ * N
where F_friction is the force of friction, μ is the coefficient of static friction, and N is the normal force.
First, let's calculate the normal force by using the formula:
N = m * g
where N is the normal force, m is the mass of the body, and g is the acceleration due to gravity.
Given:
- The mass of the body, m = 25 kg
- The acceleration due to gravity, g = 10 m/s²
Substituting these values into the formula, we can find:
N = m * g
N = 25 kg * 10 m/s²
N = 250 kg m/s²
Now, we need to find the force of friction, F_friction. The force of friction is equal to the product of the coefficient of static friction and the normal force. From the given data, the body was brought to rest, which means the force of friction is equal and opposite to the force that was initially propelling the body:
F_friction = m * a
where F_friction is the force of friction, m is the mass, and a is the acceleration.
Given:
- The mass of the body, m = 25 kg
- The initial velocity, u = 3.0 m/s
- The final velocity, v = 0 m/s
- The distance traveled, d = 2.5 m
The acceleration can be found using the formula:
v² = u² + 2 * a * d
Solving for a:
0² = (3.0 m/s)² + 2 * a * (2.5 m)
0 = 9 m²/s² + 5 a
Rearranging the equation:
5 a = -9 m²/s²
a = -9 m²/s² / 5
a = -1.8 m/s²
Since the acceleration is negative, this indicates deceleration, or slowing down.
Now that we have the acceleration, we can calculate the force of friction:
F_friction = m * a
F_friction = 25 kg * (-1.8 m/s²)
F_friction = -45 N
The force of friction is negative because it opposes the motion of the body.
Finally, we can find the coefficient of static friction using the equation:
F_friction = μ * N
Rearranging the formula to solve for μ:
μ = F_friction / N
μ = -45 N / 250 kg m/s²
μ = -0.18
Therefore, the coefficient of static friction is approximately -0.18.