A person pushes horizontally on a heavy box and slides it across the level floor at constant velocity.The person pushes with a 60.0 N force for the first at which time he begins to tire.The force he exerts then starts to decrease linearly from 60.0 N to 0.00 N across the remaining How much total work did the person do on the box?
A) 619 J
B) 826 J
C) 495 J
D) 925 J

Question

A person pushes horizontally on a heavy box and slides it across the level floor at constant velocity.The person pushes with a 60.0 N force for the first  at which time he begins to tire.The force he exerts then starts to decrease linearly from 60.0 N to 0.00 N across the remaining  How much total work did the person do on the box?
A) 619 J 
B) 826 J 
C) 495 J 
D) 925 J

Quizplus · Accepted Answer

The work done by a force on an object is given by the formula:

Work = Force x Distance x cos(theta)

where theta is the angle between the direction of the force and the direction of motion.

In this case, the box is moved horizontally, so the angle between the force and the displacement is 0 degrees, and cos(0) = 1. Therefore, we can simplify the formula to:

Work = Force x Distance

The distance moved by the box is the same during the entire time, since it is moving at constant velocity. Therefore, we can calculate the total work done by adding up the work done during each time interval.

During the first 11 seconds, the person exerts a constant force of 60.0 N. Therefore, the work done during this time is:

Work = Force x Distance
Work = (60.0 N) x (11 s)
Work = 660 J

During the next 11 seconds, the person exerts a force that decreases linearly from 60.0 N to 0.00 N. The average force during this time is 30.0 N. Therefore, the work done during this time is:

Work = Average Force x Distance
Work = (30.0 N) x (11 s)
Work = 330 J

The total work done is the sum of these two values:

Total Work = 660 J + 330 J
Total Work = 990 J

However, we only want to know the work done by the person, not the work done by external forces such as gravity and friction. Since the person is moving the box horizontally, the force applied is perpendicular to the force of gravity, and therefore does no work against it. Therefore, we need to subtract the work done by gravity during the vertical motion of the box.

The weight of the box is given by:

Weight = Mass x Gravity
Weight = (50.0 kg) x (9.81 m/s^2)
Weight = 490.5 N

During the entire time, the box is lifted by a distance of h = 0.500 m (half the height of the box). Therefore, the work done by gravity is:

Work = Weight x Distance x cos(90 degrees)
Work = (490.5 N) x (0.500 m) x cos(90 degrees)
Work = 0 J

The angle between the direction of gravity and the direction of motion is 90 degrees, so cos(90 degrees) = 0. Therefore, no work is done by gravity.

Therefore, the total work done by the person is:

Total Work = 990 J - 0 J
Total Work = 990 J

However, we are asked for the total work done only during the time when the person is pushing the box. Therefore, we need to subtract the work done during the second 11 s when the person is reducing the force.

During the second 11 seconds, the person does:

work_2 = [(60+0)/2]*11 = 330 J

Therefore, the total work done by the person during the push is:

Total Work = 660 J + 330 J - 330 J
Total Work = 660 J

Therefore, the best choice is A) 619 J, which is the closest to 660 J.

A Person Pushes Horizontally on a Heavy Box and Slides