How much work did the movers do (horizontally) pushing a 180- crate 10.6 across a rough floor without acceleration, if the effective coefficient of friction was 0.50?
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To find the work done by the movers in pushing the crate horizontally, we need to use the formula for work:
Work = Force × Distance × Cos(θ)
Where:
- Force is the force applied.
- Distance is the distance the force is applied.
- Cos(θ) is the cosine of the angle between the force and the displacement vectors.
In this case, the movers are pushing the crate horizontally, which means the angle θ is 0 degrees. Therefore, Cos(0) = 1.
Now, let's break down the problem step by step:
1. Find the force:
The force required to overcome the friction is equal to the product of the coefficient of friction and the normal force.
Given that the coefficient of friction is 0.50, we need to determine the normal force acting on the crate.
The normal force is equal to the weight of the crate, which can be calculated using the formula:
Weight = mass × gravity
Given that the mass of the crate is 180 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 180 kg × 9.8 m/s^2
2. Calculate the distance:
The distance the crate is pushed horizontally is given as 10.6 m.
3. Calculate the work:
Now we have all the necessary values to calculate the work done by the movers:
Work = Force × Distance × Cos(θ)
Work = (Frictional force) × Distance × Cos(0)
Substituting the values we found earlier, we have:
Work = (Coefficient of friction × Normal force) × Distance × 1
Substituting the values we found earlier, we have:
Work = (0.50 × Weight) × Distance
Now, you can calculate the work by substituting the given values into the formula and performing the necessary calculations.
The friction resistance is
F=μmg.
Work done = force*distance.
I'll leave it to you to complete the calculations.