To find the coefficient of friction, we can start by calculating the work done against friction using the given force and distance.
The work done against friction can be calculated using the formula:
Work = Force × Distance
Given: Force applied (F) = 350 N Distance (d) = 20 m
Work = 350 N × 20 m Work = 7000 J (joules)
Now, we need to determine the energy expended. In this case, the work done against friction represents the energy expended in moving the piano across the floor. So, the energy expended is 7000 joules.
The coefficient of friction (μ) can be determined using the formula:
Frictional Force = Normal Force × Coefficient of Friction
Given: Frictional Force (Ff) = 7000 N (since the piano is moved horizontally against friction) Normal Force (Fn) = 1000 N (weight of the piano)
7000 N = 1000 N × μ
Now, we can solve for the coefficient of friction:
μ = 7000 N / 1000 N μ = 7
Therefore, the coefficient of friction in this case is 7.
It's worth noting that a coefficient of friction of 7 is exceptionally high. It's possible that there was an error in the calculation or the provided information. Normally, the coefficient of friction is a non-dimensional value typically between 0 and 1, representing the ratio of the frictional force to the normal force.