A 107 kg clock initially at rest on a horizontal floor requires a 673 N horizontal force to set it in motion. After the clock is in motion, a horizontal force of 522 N keeps it moving with a constant velocity.
(a) Find ìs between the clock and the floor.
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(b) Find ìk between the clock and the floor.
I thought I was doing the work right and everything but I just can't seem to get the right answer. Help please!
To solve this problem, we can use the concept of frictional forces. Let's break it down step by step:
(a) Find µs between the clock and the floor:
The force required to set the clock in motion is the maximum static friction force. Therefore, we can equate this force to the product of the coefficient of static friction µs and the normal force N, which is the weight of the clock.
The normal force N is equal to the weight of the clock, given by the mass (m) of the clock multiplied by the acceleration due to gravity (g). In this case, m = 107 kg and g = 9.8 m/s².
So, N = m * g = 107 kg * 9.8 m/s² = 1048.6 N.
Therefore, the equation for static friction is:
Highest horizontal force = µs * N
673 N = µs * 1048.6 N
Now, let's solve for µs:
µs = 673 N / 1048.6 N
(b) Find µk between the clock and the floor:
Once the clock is in motion, the force required to keep it moving with a constant velocity is the kinetic friction force.
The kinetic friction force is given by the equation:
Force of kinetic friction = µk * N
To find µk, we can use the force required to keep the clock moving:
Force of kinetic friction = 522 N
Using the same weight for the normal force N as in part (a), we can rewrite the equation:
522 N = µk * 1048.6 N
Now, let's solve for µk:
µk = 522 N / 1048.6 N
By substituting the given values into the equations above, you should be able to correctly calculate both µs and µk.