A bicyclist rides 2.78 km due east, while the resistive force from the air has a magnitude of 6.52 N and points due west. The rider then turns around and rides 2.78 km due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of 6.52 N and points due east. Find the work done by the resistive force during the round trip.
hmu
To find the work done by the resistive force during the round trip, we need to calculate the work done on each leg of the journey separately and then sum them.
The work done by a force can be calculated using the formula:
Work = Force * Distance * cos(theta)
where Force is the magnitude of the force, Distance is the distance over which the force is applied, and theta is the angle between the force vector and the direction of motion.
First, let's calculate the work done on the first leg of the trip (going east):
Force = 6.52 N (given)
Distance = 2.78 km = 2.78 * 1000 m = 2780 m
Here, the force and the direction of motion are in opposite directions, so the angle between them is 180 degrees or pi radians.
theta = 180 degrees = pi radians
Now we can calculate the work:
Work1 = 6.52 N * 2780 m * cos(pi radians)
Next, let's calculate the work done on the second leg of the trip (going west):
Force = 6.52 N (given)
Distance = 2.78 km = 2.78 * 1000 m = 2780 m
Here, the force and the direction of motion are in the same direction, so the angle between them is 0 degrees or 0 radians.
theta = 0 degrees = 0 radians
Now we can calculate the work:
Work2 = 6.52 N * 2780 m * cos(0 radians)
Finally, we can find the total work done by summing the two works:
Total Work = Work1 + Work2
Plug in the calculated values to get the final answer.