A rope attached to a truck pulls a 180-kg motorcycle at 9.0 m/s. The rope exerts a 400-N force on the motorcycle at an angle of 15∘ above the horizontal.
What is the work that the rope does in pulling the motorcycle 300 m?
Express your answer with the appropriate units.
work= force*distance=400cosine15*300
300
To find the work done by the rope in pulling the motorcycle, we need to use the formula:
Work = Force * Distance * cos(theta)
Where:
Force = 400 N (force exerted by the rope)
Distance = 300 m (distance traveled by the motorcycle)
theta = 15° (angle above the horizontal)
First, we need to find the horizontal component of the force exerted by the rope. We can do this by using the angle and the given force:
Horizontal component of force = Force * cos(theta)
Horizontal component of force = 400 N * cos(15°)
Next, we can substitute the values we have into the formula for work:
Work = (400 N * cos(15°)) * 300 m
To calculate this, you can use a calculator or do the following steps:
1. Convert the angle from degrees to radians: 15° * (π/180°) = 0.2618 radians
2. Calculate the cosine of the angle: cos(0.2618 radians) ≈ 0.9659
3. Substitute the values: Work = (400 N * 0.9659) * 300 m
Now, we can calculate the work:
Work ≈ (386.36 N) * 300 m
Multiplying these values together:
Work ≈ 115,908 J (joules)
Therefore, the work done by the rope in pulling the motorcycle 300 m is approximately 115,908 joules.