A mass of 300 g is attached to a string that is 1.21 m in length. The mass is whirled in a horizontal circle on a surface and completes 7.00 rotations in a time of 2.71 s. The force of tension in the string is 92.7 N. Determine the force of friction between the mass and the surface.

To determine the force of friction between the mass and the surface, we can use the concept of centripetal force. In this case, the force of tension in the string provides the centripetal force needed to keep the mass moving in a circle.

The centripetal force (F) can be calculated using the following formula:

F = (m * v^2) / r

Where:
- m is the mass of the object (0.3 kg)
- v is the linear velocity of the object
- r is the radius of the circle (1.21 m)

To find the linear velocity, we can use the formula:

v = (2π * r * n) / t

Where:
- n is the number of rotations (7.00 rotations)
- t is the time taken to complete the rotations (2.71 s)

First, let's find the linear velocity (v):

v = (2π * 1.21 m * 7.00 rotations) / 2.71 s
v ≈ 16.632 m/s

Now, we can substitute the values of mass (m), linear velocity (v), and radius (r) into the centripetal force formula to calculate the force of tension (F):

F = (0.3 kg * (16.632 m/s)^2) / 1.21 m
F ≈ 71.885 N

Given that the force of tension in the string is 92.7 N, we can subtract this value from the calculated centripetal force (F) to find the force of friction (f):

f = 92.7 N - 71.885 N
f ≈ 20.815 N

Therefore, the force of friction between the mass and the surface is approximately 20.815 N.