What is the work done by the movers on the chest when they lift it straight up 1.0 m compared to sliding it up the 4.0-m-long the frictionless ramp?
the ramp (frictionless) is a longer distance, but a lower effort (force)
the work is the same
To determine the work done by the movers in both scenarios, we need to use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Force is the applied force on the object,
- Distance is the displacement of the object,
- θ is the angle between the force and the direction of motion.
First, let's consider the case where the movers lift the chest straight up.
In this scenario, the displacement (distance) is 1.0 m, and the angle θ is 0 degrees since the force is acting straight up along the displacement. Additionally, the chest is lifted vertically, so the applied force is equal to the weight of the chest.
To calculate the work, we need to determine the weight of the chest, which is given by the formula:
Weight = mass × acceleration due to gravity
Since the ramp is frictionless, there is no force against the motion, and thus the normal force and weight are the only forces acting vertically. Therefore, the weight of the chest remains the same in both cases.
Now let's consider the case where the movers slide the chest up the frictionless ramp.
In this case, the displacement (distance) is 4.0 m, and the angle θ is 0 degrees, as the applied force is acting parallel to the displacement.
Again, the weight of the chest is equal to the applied force in this scenario as well.
To calculate the work done in both cases, we need to compute the weight of the chest and then multiply it by the respective distances:
Work = Weight × Distance × cos(θ)
Since the weight remains the same in both cases, the only difference is the distance traveled.
Therefore, the work done by the movers when lifting the chest straight up 1.0 m is equal to the work done by sliding it up the 4.0 m frictionless ramp.