A dim but resourceful student has a summer job in a factory moving boxes. The 50 kg student finds that if he runs at a speed of 5.8 m/s and then dives head first into the boxes, he can move them across the floor. If the boxes have a mass of 65 kg and the force of friction between the boxes and the floor is 382 N, how far will he move the boxes after hitting it six times?
To find out how far the student will move the boxes after hitting them six times, we need to calculate the distance traveled in each individual hit and then add them up.
To determine the distance traveled in one hit, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy:
Work done = Change in kinetic energy
The work done against friction (the force opposing the motion) can be calculated as:
Work done against friction = Force of friction × Distance
The work done by the student to move the boxes can be calculated using the formula for work:
Work done by the student = Force by the student × Distance
Since the work done by the student is equal to the work done against friction, we can set these two equations equal to each other:
Force by the student × Distance = Force of friction × Distance
Now, we can solve for the distance traveled in each hit.
First, we need to calculate the force exerted by the student on the boxes. We can use Newton's second law:
Force by the student = Mass of the student × Acceleration
The acceleration can be calculated using the formula for acceleration:
Acceleration = Change in velocity / Time taken
The change in velocity can be calculated using the initial velocity (5.8 m/s) and the final velocity (0 m/s) after hitting the boxes. The time taken can be calculated by using the average speed (5.8 m/s) and the distance traveled in each hit.
Now, we can plug the values into these formulas to calculate the distance traveled in each hit. Then, we can add up the distances from each hit to get the total distance the boxes will be moved after six hits.
Let's do the calculations step by step:
1. Calculate the force exerted by the student:
Force by the student = Mass of the student × Acceleration
2. Calculate the change in velocity:
Change in velocity = Final velocity − Initial velocity
3. Calculate the time taken:
Time taken = Distance / Average speed
4. Calculate the distance traveled in each hit:
Distance = Average speed × Time taken
5. Add up the distances from each hit to get the total distance the boxes will be moved after six hits.
Now, you can use these steps to calculate the final answer.