A horizontal force of 804 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 32° (from the horizontal).
(a) What force do you exert on the rope?
1 N
(b) How much work do you do on the crate if you move it 22 m?
2 J
(c) If you complete the job in 8.0 s, what power is developed?
3 kW
To answer these questions, we need to break down the given information and use some relevant physics concepts.
(a) What force do you exert on the rope?
To find the force you exert on the rope, we need to consider the horizontal and vertical components of the force exerted by the rope.
The horizontal component of the force is responsible for the crate's movement, while the vertical component contributes to the normal force and gravitational force but doesn't affect the movement.
The horizontal force needed to drag the crate is given as 804 N. The force you exert on the rope can be found using trigonometry.
The horizontal component of the force is given by:
Horizontal force = Force on the rope * cos(angle)
We can substitute the given values into the equation:
Force on the rope = 804 N / cos(32°)
Calculating the value:
Force on the rope ≈ 938.35 N
So, the force you exert on the rope is approximately 938.35 N.
(b) How much work do you do on the crate if you move it 22 m?
The work done on an object can be calculated using the formula:
Work = Force * Distance * cos(angle)
Here, the force can be the force you exert on the rope, which was calculated as 938.35 N. The distance is given as 22 m. The angle in this case is the same as the angle at which the rope is held, which is 32°.
Substituting the values:
Work = 938.35 N * 22 m * cos(32°)
Calculating the value:
Work ≈ 17104 J
So, the work done on the crate is approximately 17104 J.
(c) If you complete the job in 8.0 s, what power is developed?
Power can be calculated using the formula:
Power = Work / Time
We already have the value of work from the previous question as 17104 J. The time is given as 8.0 s.
Substituting the values:
Power = 17104 J / 8.0 s
Calculating the value:
Power ≈ 2138 W
Since 1 kW = 1000 W, we can convert the power to kilowatts:
Power ≈ 2.138 kW
So, the power developed is approximately 2.138 kW.
A. is correct but B. and C. is incorrect trust me....
(a) Well, if you're holding a rope at an angle of 32°, I hope you're putting in some effort! The force you exert on the rope can be found using some trigonometry. The horizontal component of the force can be found by multiplying the total force by the cosine of the angle. So, the force you exert on the rope is 804 N * cos(32°) = 682.69 N. That's a lot of pulling power!
(b) Moving on to the work done, we can calculate it using the formula: work = force * distance * cosine(angle). Plugging in the values, we get work = 804 N * 22 m * cos(32°) = 15901.49 J. That's some serious work you're putting in!
(c) To find the power developed, we can use the formula: power = work / time. Plugging in the values, we get power = 15901.49 J / 8.0 s = 1987.69 W. So, you are developing a power of 1987.69 watts. That's almost 2 kilowatts! Look out, world, here comes the power clown!
(a) To find the force you exert on the rope, we need to resolve the force into horizontal and vertical components.
The horizontal component of the force can be found using trigonometry:
F_horizontal = F * cos(angle)
F_horizontal = 804 N * cos(32°) ≈ 675.67 N
Therefore, the force you exert on the rope is approximately 675.67 N.
(b) The work done on the crate can be calculated using the formula:
Work = Force * Distance
Given that the force is 804 N and the distance is 22 m:
Work = 804 N * 22 m
Work ≈ 17688 J
Therefore, the work done on the crate is approximately 17688 J.
(c) Power is defined as the rate at which work is done, or the amount of work done per unit time.
Power = Work / Time
Given that the work is 17688 J and the time is 8.0 s:
Power = 17688 J / 8.0 s
Power ≈ 2211 W
Therefore, the power developed is approximately 2211 W, or 2.211 kW.
a. Fe*cos32 = 804 N.
Fe = 804 / cos32 = 948 N. = Force exerted.
b. W = Fe * d = 948 * 22 = 20,856 J.
c. P = W / t = 20,656 / 8 s. = 2607 J/s
= 2607 Watts = 2.607 KW.