a worker pushes a box with a horizontal force of 50 N over a level distance of 5m. If a frictional force of 43 N acts on the box in a direction opposite to that of the worker, what was the net work done to the box?
Work = (force) x (distance)
The worker does (50N) x (5m) = 250 joules of work.
Friction eats up (43N) x (5m) = 215 joules of that energy,
generating 215 joules of heat.
The remaining (250J - 215J) = 35 joules of energy moves the box.
To find the net work done on the box, we need to calculate the work done by the worker and subtract the work done by friction.
The work done by the worker is given by the formula:
Work = Force x Distance x cos(theta)
where:
- Force is the horizontal force exerted by the worker (50 N)
- Distance is the level distance over which the box is pushed (5 m)
- cos(theta) is the angle between the direction of the force and the direction of motion, which is 0° in this case (cos(0°) = 1)
Calculating the work done by the worker:
Work by the worker = 50 N x 5 m x cos(0°) = 250 J
The work done by friction is given by the formula:
Work = Force x Distance x cos(theta)
where:
- Force is the frictional force acting on the box (43 N)
- Distance is the level distance over which the box is pushed (5 m)
- cos(theta) is the angle between the direction of the force and the direction of motion, which is 180° in this case (cos(180°) = -1)
Calculating the work done by friction:
Work by friction = 43 N x 5 m x cos(180°) = -215 J
Finally, to find the net work done on the box, we subtract the work done by friction from the work done by the worker:
Net work done = Work by the worker - Work by friction
Net work done = 250 J - (-215 J)
Net work done = 465 J
Therefore, the net work done on the box is 465 Joules.
The net work done on an object is equal to the force applied in the direction of motion multiplied by the distance over which the force is applied. In this case, the worker applies a force of 50 N in the horizontal direction to push the box, while the frictional force acts opposite to the motion with a magnitude of 43 N.
To find the net work done, we need to calculate the total work done by the worker and subtract the work done by friction (equal to the negative of the work done by the frictional force).
1. Calculate the work done by the worker:
Work done by the worker = Force applied by the worker × Distance
Work done by the worker = 50 N × 5 m = 250 J
2. Calculate the work done by friction:
Work done by friction = Force of friction × Distance
Work done by friction = (-43 N) × 5 m = -215 J
Since work done by friction is negative, it means the frictional force acts in the opposite direction of motion, causing negative work.
3. Calculate the net work done:
Net work done = Work done by the worker + Work done by friction
Net work done = 250 J + (-215 J)
Net work done = 35 J
Therefore, the net work done on the box is 35 Joules.