What force must be applied to roll a 120-pound barrel up an inclined plane 9 feet long to a height of 3 feet?

What force must be applied to roll a 120-pound barrel up an inclined plane 9 feet long to a height of 3 feet?

• A. 30 pounds
• B. 40 pounds
• C. 50 pounds
• D. 60 pounds

Answer: (B)

Moving a weight up a slope without friction requires work equal to the weight times the height gained. The barrel weighs 120 pounds and you raise it 3 feet, so the work needed is 120 × 3 = 360 foot-pounds. The force you push along the plane, times the distance along the plane (9 feet), must equal that work: F × 9 = 360, so F = 360/9 = 40 pounds. Another way: the incline angle has sin(theta) = 3/9 = 1/3, so the component of weight along the plane is 120 × 1/3 = 40 pounds. Therefore, the required pushing force is 40 pounds. If friction were present, you'd need more.

Moving a weight up a slope without friction requires work equal to the weight times the height gained. The barrel weighs 120 pounds and you raise it 3 feet, so the work needed is 120 × 3 = 360 foot-pounds. The force you push along the plane, times the distance along the plane (9 feet), must equal that work: F × 9 = 360, so F = 360/9 = 40 pounds. Another way: the incline angle has sin(theta) = 3/9 = 1/3, so the component of weight along the plane is 120 × 1/3 = 40 pounds. Therefore, the required pushing force is 40 pounds. If friction were present, you'd need more.