A(n) 94 kg clock initially at rest on a horizontal
floor requires a(n) 697 N horizontal
force to set it in motion. After the clock is in
motion, a horizontal force of 530 N keeps it
moving with a constant velocity.
The acceleration of gravity is 9.81 m/s2
Find µk between the clock and the floor.
To find the coefficient of kinetic friction (µk) between the clock and the floor, we can use the equation:
µk = Fk / N
Where:
Fk is the force of kinetic friction
N is the normal force
The force of kinetic friction can be calculated using the equation:
Fk = µk * N
Initially, the clock is at rest, so the force required to set it in motion is equal to the force of static friction (Fs). Thus, we can write:
Fs = 697 N
After the clock is in motion, the force required to keep it moving at a constant velocity is equal to the force of kinetic friction, so:
Fk = 530 N
The normal force (N) can be calculated as the weight of the clock, which is equal to its mass (m) times the acceleration due to gravity (g):
N = m * g
Given that the mass (m) of the clock is 94 kg and the acceleration due to gravity (g) is 9.81 m/s^2, we can calculate the normal force:
N = 94 kg * 9.81 m/s^2
Now, we can substitute the values of Fs and N into the equation for the coefficient of kinetic friction:
µk = Fk / N = (530 N) / (94 kg * 9.81 m/s^2)
Calculating this expression will give us the value of µk.
To find the coefficient of kinetic friction (μk) between the clock and the floor, we can use the formula:
μk = Fk / N
where Fk is the force of kinetic friction and N is the normal force.
First, let's find the normal force (N) acting on the clock. The normal force is equal to the weight of the clock.
Weight = mass × acceleration due to gravity
Weight = 94 kg × 9.81 m/s^2
Weight = 921.14 N
Therefore, the normal force acting on the clock is 921.14 N.
To find the force of kinetic friction (Fk), we can subtract the force required to set the clock in motion from the force required to keep it moving at a constant velocity.
Fk = Force to set in motion - Force to keep it moving
Fk = 697 N - 530 N
Fk = 167 N
Now we can plug the values into the formula for the coefficient of kinetic friction:
μk = Fk / N
μk = 167 N / 921.14 N
Calculating this, the coefficient of kinetic friction between the clock and the floor is approximately 0.181.
forcefriction=uk*mg
uk=530/(98*9.8)