A horizontal force of 790 N is needed to drag a crate across a horizontal floor with a constant speed. You drag the crate using a rope held at an angle of 33° (from the horizontal).
(a) What force do you exert on the rope?
Enter a number.1 N
(b) How much work do you do on the crate if you move it 22 m?
Enter a number.2 J
(c) If you complete the job in 8.0 s, what power is developed?
Enter a number.3 kW
It appears you are answer grazing. If you want help, show your work, and we will critique your work.
To determine the force you exert on the rope, we can use some basic trigonometry principles. The force you exert on the rope can be split into two components: one that acts parallel to the floor (horizontal component) and one that acts perpendicular to the floor (vertical component).
(a) To find the force you exert on the rope, we need to determine the horizontal component of the force. This can be found by considering the angle at which the rope is held.
Cosine(angle) = Adjacent / Hypotenuse
Cos(33°) = Horizontal Component / 790 N
Rearranging the equation, we find:
Horizontal Component = Cos(33°) * 790 N
Horizontal Component ≈ 0.836 * 790 N ≈ 660.4 N
Therefore, you exert a force of approximately 660.4 N on the rope.
(b) To calculate the work done on the crate, we use the formula:
Work = Force * Distance * Cosine(angle)
Work = 790 N * 22 m * Cos(33°)
Work ≈ 790 N * 22 m * 0.836 ≈ 14,798.72 J
Therefore, the work done on the crate is approximately 14,798.72 J.
(c) Power is defined as the rate at which work is done. It can be calculated using the formula:
Power = Work / Time
Power = 14,798.72 J / 8.0 s
Power ≈ 1849.84 W
To convert watts to kilowatts, we divide by 1000:
Power ≈ 1849.84 / 1000 ≈ 1.85 kW
Therefore, the power developed is approximately 1.85 kW.