Before railroad were invented, goods often traveled along canals, with mules pulling barges from the bank. If a mule is exerting a 12,000N force for 10km, and the rope connecting the mule to the barge is at a 20 degree angle from the direction of travel, how much work did the mole do on the barge?
A. 12MJ
B. 11MJ
C. 4.1MJ
D. 6MJ
To determine how much work the mule did on the barge, we need to use the formula for work: Work = Force x Distance x cos(theta), where:
- Force is the magnitude of the force applied by the mule (12,000N).
- Distance is the distance traveled by the barge (10km).
- Theta is the angle between the direction of the force and the direction of travel (20 degrees).
First, we need to convert the distance from kilometers to meters. Since 1 kilometer is equal to 1000 meters, the distance will be 10,000 meters.
Next, we need to convert the angle from degrees to radians. To convert from degrees to radians, we use the formula: Radians = Degrees x (pi/180). Therefore, the angle in radians will be 20 degrees x (pi/180) = 20pi/180 = pi/9 radians.
Plugging these values into the formula, we have:
Work = 12,000N x 10,000m x cos(pi/9)
Using a calculator, we can find cos(pi/9) ≈ 0.9397.
Work ≈ 12,000N x 10,000m x 0.9397
Work ≈ 113,364,000 Nm
To convert this to megajoules (MJ), we divide by 1,000,000:
Work ≈ 113.364 MJ
Rounded to one decimal place, the answer is approximately 113.4 MJ.
Therefore, the correct answer choice is not listed among the options provided.