how much power is required to raise a 30 kg crate a vertical distance of 6 m in a time of 4 seconds?
a. 52.5 W
b. 120 W
c. 385 W
d. 450 W
e. 525 W
How much power is required to raise a 30 kg creat with a vertical distance of 6m in a time of seconds
To calculate the power required to raise a crate, we can use the formula:
Power = Work / Time
First, let's calculate the work done by lifting the crate:
Work = Force × Distance
The force required to lift the crate can be calculated using Newton's second law:
Force = Mass × Acceleration due to gravity
= Mass × 9.8 m/s²
Plugging in the given values:
Force = 30 kg × 9.8 m/s²
= 294 N
Now, we can calculate the work done:
Work = Force × Distance
= 294 N × 6 m
= 1764 J
Finally, to calculate the power, we divide the work by the given time:
Power = Work / Time
= 1764 J / 4 s
= 441 W
The power required to raise the 30 kg crate is 441 W. However, none of the given answer choices match this value.
To find the power required to raise the crate, we need to use the formula:
Power = Work / Time
First, let's find the work done in lifting the crate. The work done is equal to the force applied multiplied by the distance. In this case, the force is the weight of the crate, which is equal to its mass times the acceleration due to gravity (9.8 m/s²).
Work = Force × Distance
Work = (mass × acceleration due to gravity) × distance
Given:
Mass of the crate = 30 kg
Distance raised = 6 m
Work = (30 kg × 9.8 m/s²) × 6 m
Now, we can find the power using the formula:
Power = Work / Time
Given:
Time taken = 4 seconds
Power = (Work) / (Time)
Power = [(30 kg × 9.8 m/s²) × 6 m] / 4 s
Calculating this expression gives us:
Power = (1764 kg·m²/s²) / 4 s
Power = 441 J / 4 s
Power = 110.25 W
Therefore, the power required to lift the crate is approximately 110.25 W. None of the given options match this answer exactly, but the closest one is option B, which states 120 W.
power = work/time = force*distance/time
so use your numbers.