Two workers are loading crates onto a pick up truck. Worker 1 lifts his crate straight up from the ground to the truck. Worker 2 slides his crate up a ramp which has frictionless rollers. Which statement is true about the work being done on the crate?
a. Worker 1 does more work than worker 2.
b. Worker 2 does more work than worker 1.
c. Both workers do the same amount of work.
d. Can not be determined because the angle of the ramp is unknown.
e. The mass is unknown therefore none of the statements are true.
Matt. We are not going to do your thinking for you. We will be happy to guide or critique your thinking. We wouldn't want anyone to get the idea you are answer mooching.
To determine which statement is true about the work being done on the crate, we need to understand the concept of work and how it is calculated.
Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, it can be calculated as:
Work = Force × Distance × cos(θ)
Where:
- Force is the amount of force applied on the object.
- Distance is the displacement of the object in the direction of the force.
- θ is the angle between the force and the displacement vectors.
In this scenario, we can assume that both workers are exerting the same amount of force, as they are both lifting their crates onto the truck. However, the method of lifting differs for each worker.
Worker 1 lifts his crate straight up from the ground to the truck. In this case, the force exerted is vertical, and the displacement is also vertical. As a result, the angle θ in the equation is 0 degrees.
Worker 2 slides his crate up a ramp with frictionless rollers. In this case, the force exerted is at an angle to the vertical direction, which means there is an angle θ between the force and the displacement vectors.
Now, let's analyze the given options:
a. Worker 1 does more work than worker 2.
If we assume the same force and the same vertical displacement (height) for both workers, the angle θ for worker 1 is 0 degrees, and for worker 2 it is greater than 0 degrees. Since the cosine of 0 degrees is 1, and the cosine of any angle greater than 0 degrees is less than 1, worker 1 does more work than worker 2. Therefore, option a is true.
b. Worker 2 does more work than worker 1.
As explained above, worker 1 does more work than worker 2. Therefore, option b is false.
c. Both workers do the same amount of work.
As explained above, worker 1 does more work than worker 2. Therefore, option c is false.
d. Cannot be determined because the angle of the ramp is unknown.
The angle of the ramp is not necessary to determine which worker does more work. Regardless of the ramp angle, the force exerted by worker 1 will always be vertical and have a θ of 0 degrees, thus doing more work than worker 2. Therefore, option d is false.
e. The mass is unknown, therefore none of the statements are true.
The mass of the crate is not a factor in determining which worker does more work. The work done only depends on the force applied and the displacement in the direction of that force. Therefore, option e is false.
In conclusion, the correct answer is: a. Worker 1 does more work than worker 2.