A person is pulling a freight cart with a force of 70 pounds. How much work is done in moving the cart 120 feet if the cart's handle makes an angle of 18° with the ground
To calculate the work done in moving the cart, we need to use the formula:
Work = Force × Distance × Cosθ
Where:
- Work is the amount of work done
- Force is the force applied
- Distance is the distance over which the force is applied
- θ (theta) is the angle between the direction of the force and the direction of the movement
In this case, the force applied is 70 pounds, the distance is 120 feet, and the angle is 18°.
Step 1: Convert the angle from degrees to radians.
To use the formula, we need to convert the angle from degrees to radians. To do this, we can use the formula: Radians = (π / 180) × Degrees.
Angle in radians = (π / 180) × 18°
Angle in radians = 0.3142 radians (approx)
Step 2: Calculate the work using the formula.
Work = Force × Distance × Cosθ
Work = 70 pounds × 120 feet × Cos(0.3142)
Work ≈ 8055.45 foot-pounds
Therefore, approximately 8055.45 foot-pounds of work is done in moving the cart 120 feet when the cart's handle makes an angle of 18° with the ground.