A 55-kg packing crate is pulled with constant speed across a rough floor with a rope that is at an angle of 41.0 ∘ above the horizontal.
If the tension in the rope is 195 N , how much work is done on the crate by the rope to move it 3.0 mm ?
Force in direction of motion = Fx = 195 cos 41
so work done = 195 cos 41 * 3 Joules
I assume you mean 3 meters, not 3 millimeters
441
To find the work done on the crate by the rope, we need to calculate the force applied by the rope and then multiply it by the distance moved.
Step 1: Resolve the force into horizontal and vertical components.
The tension in the rope can be resolved into its vertical and horizontal components using trigonometry. The vertical component (T⊥) is given by T*sinθ, where T is the tension in the rope and θ is the angle of the rope with respect to the horizontal. The horizontal component (T∥) is given by T*cosθ.
T⊥ = T * sin(θ)
T∥ = T * cos(θ)
Step 2: Calculate the work done on the crate.
To find the work done on the crate, we need to multiply the horizontal component of the tension force by the distance moved. The work done is given by the formula:
Work = Force * Distance
In this case, the force is the horizontal component of the tension force (T∥) and the distance is the displacement of the crate (3.0 mm).
Work = T∥ * Distance
Step 3: Substitute the values into the formula and calculate.
Given:
T = 195 N (tension in the rope)
θ = 41.0° (angle of the rope)
First, calculate the horizontal and vertical components of the tension force:
T⊥ = T * sin(θ)
T∥ = T * cos(θ)
Next, substitute the value of T∥ and the distance into the work formula:
Work = T∥ * Distance
Finally, calculate the work done by substituting the values and performing the calculations:
Work = T∥ * Distance
Work = (T * cos(θ)) * Distance
Work = (195 N * cos(41.0°)) * 3.0 mm
The answer will be in joules (J), which is the unit of work.