Question

A 55-kg k g packing crate is pulled with constant speed across a rough floor with a rope that is at an angle of 40.8 ∘ ∘ above the horizontal. If the tension in the rope is 155 N N , how much work is done on the crate by the rope to move it 5.0 m m ?

Answer 1

To calculate the work done on a crate pulled by a rope at an angle, we use the component of the force in the direction of motion. The work done is 155 N × 5.0 m × cos(40.8°), which equals approximately 584.7 Joules.

Step-by-step explanation:

To find the work done by the rope, we need to consider the component of the tension force that acts in the direction of the motion. This component is calculated by multiplying the tension force by the cosine of the angle between the force and the direction of motion. To calculate the work done on the crate, the equation is Work = Force × Distance × cos(θ). Where: Force is the tension in the rope, which is 155 N, Distance the crate is moved, which is 5.0 m, θ (theta) is the angle above the horizontal, which is 40.8°. Therefore, the work done on the crate by the rope is Work = 155 N × 5.0 m × cos(40.8°). Using a calculator, we find that: Work ≈ 155 N × 5.0 m × 0.7559 (cos(40.8°) approximately). Work ≈ 584.7 J (Joules). The work done on the crate by the rope is approximately 584.7 Joules.