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?
To find the amount of work done by the movers in pushing the crate horizontally across the rough floor, we need to consider the force exerted by the movers and the displacement of the crate. The work done can be calculated using the formula:
Work = Force x Distance x cos(θ),
where Force is the force exerted by the movers, Distance is the displacement of the crate, and θ is the angle between the force applied and the direction of displacement.
In this case, the crate is being pushed horizontally, so the angle between the force and the direction of displacement is 0 degrees. Therefore, cos(θ) = cos(0) = 1.
The force exerted by the movers can be calculated using Newton's second law of motion:
Force = mass x acceleration,
where mass is the mass of the crate and acceleration is the acceleration of the crate.
Since the crate is not accelerating, the net force on the crate must be zero. The force of friction opposes the motion, so we have:
Force of friction = μ * Normal force,
where μ is the coefficient of friction and Normal force is the force exerted by the floor on the crate in the vertical direction. In this case, since the crate is not accelerating vertically, Normal force = weight of the crate.
Weight of the crate = mass x gravitational acceleration.
Substituting these values, we get:
Force of friction = μ * (mass x gravitational acceleration).
Now, we can calculate the force exerted by the movers:
Force = Force of friction = μ * (mass x gravitational acceleration).
Finally, we can substitute these values into the work formula:
Work = Force x Distance x cos(θ) = (μ * (mass x gravitational acceleration)) * Distance * cos(θ).
Plugging in the given values:
mass = 140 kg
Distance = 10.1 m
μ = 0.60
gravitational acceleration = 9.8 m/s²
we can calculate the work done by the movers.