A 93 kg clock initially at rest on a horizontal floor requires a 614 N horizontal force to set it in motion. After the clock is in motion, a horizontal force of 510 N keeps it moving with a constant velocity.
Find μs between the clock and the floor.
Find μk between the clock and the floor.
force friction=forces above=mu*mg
static:
614=mu*93*g solve for mu.
dynamic: you do it.
To find the coefficient of static friction (μs) between the clock and the floor, we can use the equation:
μs = F_s / N
where F_s is the force of static friction, and N is the normal force.
Given that the clock has a mass of 93 kg, we can calculate the normal force using the equation:
N = m * g
where m is the mass of the clock and g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = 93 kg * 9.8 m/s^2 = 911.4 N
Next, we need to find the force of static friction required to set the clock in motion. This force is equal to the applied force required to overcome static friction:
F_s = 614 N
Substituting these values into the equation for μs:
μs = F_s / N = 614 N / 911.4 N ≈ 0.674.
Therefore, the coefficient of static friction (μs) between the clock and the floor is approximately 0.674.
Now, let's find the coefficient of kinetic friction (μk) between the clock and the floor. The force of kinetic friction can be calculated using the equation:
F_k = μk * N
Given that a force of 510 N is required to keep the clock moving at a constant velocity, we can substitute the values into the equation:
F_k = 510 N
N = 911.4 N
510 N = μk * 911.4 N
Simplifying the equation:
μk = 510 N / 911.4 N ≈ 0.559
Therefore, the coefficient of kinetic friction (μk) between the clock and the floor is approximately 0.559.
To find the static friction coefficient (μs) between the clock and the floor, we can use the equation:
Fs = μs * N
Where Fs is the force of static friction and N is the normal force between the clock and the floor. Since the clock is initially at rest, the force required to set it in motion is equal to the force of static friction.
Given that the force required to set the clock in motion is 614 N, we have:
Fs = 614 N
The normal force (N) between the clock and the floor is equal to the weight of the clock, which can be calculated as:
N = m * g
Where m is the mass of the clock and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the clock is 93 kg, we have:
N = 93 kg * 9.8 m/s^2 = 911.4 N
Now we can substitute the values of Fs and N into the equation to solve for μs:
614 N = μs * 911.4 N
μs = 614 N / 911.4 N ≈ 0.674
Therefore, the static friction coefficient (μs) between the clock and the floor is approximately 0.674.
To find the kinetic friction coefficient (μk) between the clock and the floor, we can use the equation:
Fk = μk * N
Where Fk is the force of kinetic friction. The force of kinetic friction is the force required to keep the clock moving at a constant velocity, which is given as 510 N.
Using the same normal force value (N = 911.4 N) as before, we can substitute the values into the equation to solve for μk:
510 N = μk * 911.4 N
μk = 510 N / 911.4 N ≈ 0.559
Therefore, the kinetic friction coefficient (μk) between the clock and the floor is approximately 0.559.