Final answer:
The work done on the cart when a 100 N force moves it at a 30 degree angle for 3.0 m is calculated using the formula Work = Force × Distance × cos(θ), which results in 259.8 Joules. None of the provided options match this value.
Step-by-step explanation:
To calculate the work done on the cart, we need to use the formula for work when a force is applied at an angle:
Work = Force × Distance × cos(θ)
Where:
- Force is the push or pull applied (in newtons, N)
- Distance is how far the object moves because of the force (in meters, m)
- θ (theta) is the angle the force is applied at relative to the direction of motion
- cos is the cosine function from trigonometry
Here, the force is 100 N, the distance is 3.0 m, and the angle is 30 degrees. When we plug these values into the formula, we get:
Work = 100 N × 3.0 m × cos(30°) = 100 N × 3.0 m × 0.866
Work = 259.8 Joules
None of the given options match this value precisely, but we can see that the correct answer is not listed. Always double-check the calculations, and if discrepancy remains, it could be due to an error in the question or the answer choices.