A 50-N force acts on a 2-kg crate that starts from rest. When the force has been acting for 2 s the rate at which it is doing work is:
I found this question online so I saw the answer is 2500 Watts. What I don't understand is how to come to this conclusion. Power = Work/time. The time is known but to find Work we need both the force and distance. How do I go about finding them? I assume I have to use that mass value somewhere in here, just not sure where.
It is a pleasure to help you with this; thank you for showing your work and thought process. Thank you for using Jiskha
instantaneous Power delivered by a moving force equals:
P = force x velocity
The final velocity in this case is
Vf = (1/m)*(final momentum) = F*t/m
= 50*2/2 = 50 m/s
Power at end of interval = F*Vf = 50*50 = 2500 W
The reason you got a different number is that you were calculating the AVERAGE power during the 2 second interval. The average is half the final value while the acceleration continues.
July 3rd 2021, almost 11 years later, I had the same problem with this. Thank you so much for showing the exact purpose of both formulas
Well, well, well! Looks like we have a work-related problem, huh?
To figure out the rate at which the force is doing work, we need to calculate the work done first. And to calculate work, we can use the formula:
Work = Force × Displacement × cosθ
Where θ is the angle between the force and the displacement. In this case, let's assume the force is acting along the direction of displacement, so the angle θ is zero. So cosθ = 1.
Since the crate starts from rest, we know its initial velocity is zero. Therefore, we can use the equation of motion:
Displacement = (1/2) × acceleration × time^2
We need to find the acceleration. Using Newton's second law (F = ma), we can rearrange it to find acceleration:
a = F/m
Substituting the given values, we have:
a = 50 N / 2 kg = 25 m/s^2
Now, let's calculate the displacement:
Displacement = (1/2) × 25 m/s^2 × (2 s)^2
= (1/2) × 25 m/s^2 × 4 s^2
= 50 m
Now that we have the force and displacement, we can calculate the work:
Work = 50 N × 50 m × cos(0)
= 50 N × 50 m × 1
= 2500 J
Finally, we can find the power, which is the rate at which work is done:
Power = Work / time
= 2500 J / 2 s
= 1250 W
Oops! It seems like I made an error in my calculation earlier. Sorry about that! So, the correct answer should be 1250 Watts, not 2500 Watts. I must have gotten a little carried away. Keep in mind that even Clown Bots make mistakes sometimes. I hope my explanation still brought a smile to your face!
To find the rate at which work is being done, we need to calculate the work done in a given time. Work is defined as the product of force and displacement in the direction of the force.
In this case, we are given a force of 50 N acting on a 2 kg crate. We can use Newton's second law, F = ma, to determine the acceleration of the crate. Since the crate starts from rest, its initial velocity is 0 m/s. Therefore, the force can be rearranged to find the acceleration:
F = ma => 50 N = 2 kg * a
Solving for a, we get:
a = 50 N / 2 kg
a = 25 m/s^2
Now we can find the displacement of the crate after 2 seconds. Since the crate starts from rest with an acceleration of 25 m/s^2, we can use the kinematic equation:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity (0 m/s in this case)
a = acceleration
t = time (2 seconds in this case)
Plugging in the values:
s = 0 * 2 + (1/2) * 25 * (2)^2
s = 0 + (1/2) * 25 * 4
s = 0 + 50
s = 50 meters
Now that we have the force (50 N) and displacement (50 meters), we can find the work done:
Work = Force * Displacement
Work = 50 N * 50 m
Work = 2500 N·m (Newton-meter, which is equivalent to Joules)
Finally, to find the power (rate of doing work), we need to divide the work by the time:
Power = Work / Time
Power = 2500 N·m / 2 s
Power = 1250 Watts
Therefore, the correct answer is 1250 Watts, not 2500 Watts as you mentioned.
I was able to figure some things out. Like a = F/m = 50/2 = 25 m/s^2
s=Vo +.5at^2 = .5*25*2^2 = 50 m
Work = 50*50 = 2500 J
Power = Work/time = 2500/2 = 1250 W
Problem is that the answer is 2500, but the multiple choice answers are all in Watts so that has to mean Power. What did I do wrong because either way I look at it, the answer is 1250 W for Power.