How much work did the movers do horizontally pushing a 160-kg crate 10.3m across a rough floor without acceleration, if the coefficient of friction was 0.50?
To determine the amount of work done by the movers horizontally, we need to consider the force applied, the distance, and the coefficient of friction.
First, let's calculate the force of friction acting on the crate. The force of friction can be found by multiplying the coefficient of friction (μ) by the normal force (N). In this case, the normal force is equal to the weight of the crate (mg).
Weight (W) = mass (m) × gravitational acceleration (g)
Given that the mass (m) of the crate is 160 kg and the gravitational acceleration (g) is approximately 9.8 m/s^2, we can calculate the weight:
W = 160 kg × 9.8 m/s^2 = 1568 N
Now, let's calculate the force of friction (F_friction):
F_friction = μ × N
Given that the coefficient of friction (μ) is 0.50, we can calculate the force of friction:
F_friction = 0.50 × 1568 N = 784 N
To find the amount of work done by the movers, we use the formula for work:
Work (W) = force (F) × distance (d) × cos(θ)
In this case, the force applied (F) is the force of friction (F_friction), the distance (d) is 10.3 m, and the angle (θ) between the force and the displacement is 0 degrees (cos(0) = 1).
Work (W) = 784 N × 10.3 m × cos(0) = 8055.2 J
Therefore, the movers did approximately 8055.2 joules of work horizontally pushing the crate across the rough floor.