How much work did the movers do (horizontally) pushing a 140-kg crate 10.1 m across a rough floor without acceleration, if the effective coefficient of friction was 0.60?
work= frictionforce*distance
= mu*mg*distance
848.8
To calculate the work done by the movers in pushing a crate horizontally across a rough floor, we need to consider the force of friction acting against the motion.
The formula for calculating work is:
Work = Force x Distance x cos(theta)
In this case, the force of friction can be calculated using the coefficient of friction and the normal force acting on the crate. The normal force is equal to the weight of the crate (mass x gravity). The formula for calculating the force of friction is:
Force of Friction = coefficient of friction x normal force
Since the crate is being pushed horizontally without acceleration, the angle between the force of friction and the displacement is 0 degrees, so cos(theta) = 1.
Using these formulas, we can calculate the work done by the movers:
1. Calculate the normal force:
Weight = mass x gravity
Weight = 140 kg x 9.8 m/s^2
Weight = 1372 N
2. Calculate the force of friction:
Force of Friction = coefficient of friction x normal force
Force of Friction = 0.60 x 1372 N
Force of Friction = 823.2 N
3. Calculate the work done:
Work = Force x Distance x cos(theta)
Work = Force of Friction x Distance x cos(0°)
Work = 823.2 N x 10.1 m x 1
Work = 8322.72 Joules (J)
Therefore, the movers did 8322.72 Joules of work pushing the 140-kg crate 10.1 m horizontally across the rough floor.