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. How much power is required?
d = 12m
m = 5kg
t = 15s
P = ?
P = F.v
F = mg
F = (5kg)(9.81m/s2)
F = 49.05N
v = d/t
v = 12m/15s
v = 0.8m/s
P = F.v
P = (49.05N)(0.8m/s)
P = 39.24watt
To determine the power required to raise the bucket of water, we can use the formula:
Power = Work / Time
First, let's calculate the work done in lifting the bucket of water. The work done is equal to the force applied multiplied by the distance over which the force is applied. The force applied is equal to the weight of the bucket and the water.
The weight can be calculated using the formula:
Weight = Mass * Acceleration due to gravity
In this case, the mass of the bucket and water is given as 5.00 kg.
Acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 5.00 kg * 9.8 m/s^2 = 49 N (Newtons)
Now, let's calculate the work done in lifting the bucket of water. The work (W) is equal to the weight multiplied by the distance lifted. The distance lifted is the depth of the well, which is given as 12 m.
Work = Weight * Distance = 49 N * 12 m = 588 J (Joules)
Now we can calculate the power using the formula mentioned earlier:
Power = Work / Time
Given that the time taken to raise the bucket is 15 seconds:
Power = 588 J / 15 s = 39.2 W (Watts)
Therefore, the power required to raise the bucket of water to the top of the well is approximately 39.2 Watts.