You raise a bucket of water from the bottom of a well that is 12 m deep. The mass of the bucket and the water is 5.00 kg, and it takes 15 s to raise the bucket to the top of the well.
Part A
How much power is required?
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To find the power required to raise the bucket of water, we can use the formula:
Power = Work / Time
Work is the product of the force and the distance, and in this case, the force is equal to the weight of the bucket and water. The distance is the height of the well.
First, let's calculate the force:
Force = mass x acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Force = 5.00 kg x 9.8 m/s^2 = 49 N
Next, let's calculate the work:
Work = force x distance
Distance = 12 m
Work = 49 N x 12 m = 588 J
Finally, let's calculate the power:
Power = 588 J / 15 s = 39.2 W
Therefore, the power required to raise the bucket of water is 39.2 Watts.
To calculate the power required to raise the bucket of water, we need to use the formula:
Power = Work / Time
The work done is equal to the force applied multiplied by the distance moved. In this case, the force is the weight of the bucket and water, and the distance is the depth of the well.
Step 1: Calculate the work done.
Work = Force x Distance
The force is equal to the weight of the bucket and water, which is given by:
Force = mass x gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
Step 2: Calculate the power.
Power = Work / Time
Now let's plug in the values:
Mass of bucket and water = 5.00 kg
Depth of the well = 12 m
Time taken = 15 s
Gravitational acceleration = 9.8 m/s^2
Step 1:
Force = 5.00 kg x 9.8 m/s^2
Step 2:
Work = Force x Distance
Work = (5.00 kg x 9.8 m/s^2) x 12 m
Step 3:
Power = Work / Time
Power = [(5.00 kg x 9.8 m/s^2) x 12 m] / 15 s
To find the result, calculate the expression in the brackets first and then divide by 15:
Force = 5.00 kg x 9.8 m/s^2 = 49 N
Work = 49 N x 12 m = 588 J
Power = 588 J / 15 s = 39.2 W
Therefore, the power required to raise the bucket of water is 39.2 Watts.