Charlie pulls horizontally to the right on a wagon with a force of 37.2 N. Sara pulls horizontally to the left with a force of 22.4 N. How much work is done on the wagon after it has moved 2.50 meters to the right? in joules?
2.5(37.2-22.4)
To find the work done on the wagon, we can use the formula:
Work = Force × Distance × cos(θ)
where:
- Work is the amount of work done (in joules, J),
- Force is the magnitude of the applied force (in newtons, N),
- Distance is the distance traveled in the direction of the applied force (in meters, m),
- θ is the angle between the force and the direction of motion (in degrees).
In this case, since the forces are applied horizontally and in opposite directions, the angle between the forces and the direction of motion is 180 degrees. Therefore, cos(θ) = -1.
Now, substituting the given values:
Force by Charlie = 37.2 N
Force by Sara = 22.4 N
Distance = 2.50 m
cos(θ) = -1
Now, calculate the work done by each person:
Work by Charlie = 37.2 N × 2.50 m × (-1) = -93 J
Work by Sara = 22.4 N × 2.50 m × (-1) = -56 J
Note that since the forces are in opposite directions, the work done by Charlie and Sara will have opposite signs.
To find the total work done on the wagon, we need to add the work done by both individuals:
Total Work = Work by Charlie + Work by Sara
Total Work = -93 J + (-56 J)
Finally, performing the addition:
Total Work = -149 J
Therefore, the work done on the wagon after it has moved 2.50 meters to the right is -149 joules.