A 88 arrow is fired from a bow whose string exerts an average force of 110 on the arrow over a distance of 74 .
To find the work done on the arrow by the bow's string, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done on the arrow (in joules),
- Force is the average force exerted by the bow's string (in newtons),
- Distance is the distance over which the force is applied (in meters),
- θ is the angle between the force and the direction of motion.
From the given information:
- Force = 110 N
- Distance = 74 m
However, the angle between the force and the direction of motion (θ) is not provided. If we assume that the force is applied parallel to the direction of motion, then the angle θ would be 0 degrees, and cos(θ) would be 1. In this case, we can calculate the work done as follows:
Work = 110 N × 74 m × cos(0°)
Work = 110 N × 74 m × 1
Work = 8140 joules
Thus, the work done on the arrow by the bow's string is 8140 joules.
To find the work done on the arrow by the bow string, you can use the work formula:
Work = Force × Distance × cos(θ)
In this case, the force exerted by the bow string is 110 N and the distance over which the force is applied is 74 m. However, we need to find the angle θ between the force and the direction of the displacement.
Since the arrow is being fired from a bow, we can assume that the force is applied in the same direction as the displacement of the arrow. In this case, θ would be 0 degrees, and the cosine of 0 degrees is 1.
Therefore, we can calculate the work using the formula:
Work = 110 N × 74 m × cos(0)
Since cos(0) is equal to 1, the cosine term can be omitted, and the work done on the arrow is simply:
Work = 110 N × 74 m
Now we can calculate the value:
Work = 8140 N·m
So, the work done on the arrow by the bow string is 8140 joules.