Calculate the time taken by a water pump of power 500 W to lift 2000 kg of water
to a tank, which is at a height of 15 m from the ground? Use: g = 10 m/s2
(
500W = 500J/s
work = Force * distance = 2000kg*10*15m = 300000J
300000J ÷ 500J/s = 600s = 10 minutes
Good
Well, that water pump has quite the task to accomplish! Let's see how long it'll take to get that water up 15 meters.
First, we need to calculate the gravitational potential energy of the water:
Potential energy = mass × gravity × height
PE = 2000 kg × 10 m/s² × 15 m
PE = 300,000 Joules
Now, to find the time, we can use the formula:
Power = Work / Time
Since power is given as 500 Watts and work done is equal to the potential energy (PE), we have:
500 W = 300,000 J / Time
Solving for the time:
Time = 300,000 J / 500 W
Time = 600 seconds
So, my calculations show that the water pump will take 600 seconds to lift that amount of water to a height of 15 meters. That's quite an achievement, don't you think?
To calculate the time taken by the water pump to lift the water, we can use the formula for work:
Work = Force x Distance
In this case, the force required to lift the water can be calculated using the formula:
Force = Mass x Gravity
Given:
Power of the water pump (P) = 500 W
Mass of the water (m) = 2000 kg
Height of the tank (h) = 15 m
Acceleration due to gravity (g) = 10 m/s^2
First, let's calculate the force required to lift the water:
Force = Mass x Gravity
Force = 2000 kg x 10 m/s^2
Force = 20,000 N
Next, we can calculate the work done by the water pump:
Work = Force x Distance
Work = 20,000 N x 15 m
Work = 300,000 J (Joules)
Since power is the rate at which work is done, we can use the formula:
Power = Work / Time
Rearranging the formula to find time, we get:
Time = Work / Power
Substituting the known values into the equation:
Time = 300,000 J / 500 W
Converting Watts to Joules per second:
1 Watt = 1 Joule/second
Therefore, dividing by 500 W is equivalent to dividing by 500 J/s.
Time = 300,000 J / 500 J/s
Simplifying the equation:
Time = 600 seconds
Therefore, it will take the water pump 600 seconds (or 10 minutes) to lift 2000 kg of water to a tank that is 15 m high.
To calculate the time taken by the water pump to lift the water to the tank, we can use the formula for work done:
Work = Force x Distance
First, let's calculate the force required to lift the water. The force can be found using the formula:
Force = Mass x Acceleration
Here, the mass of the water is given as 2000 kg, and the acceleration due to gravity is given as 10 m/s^2.
Force = 2000 kg x 10 m/s^2
Force = 20000 N
Next, we need to calculate the work done by the water pump. The work done is given by:
Work = Power x Time
Here, the power of the water pump is given as 500 W, and we need to find the time taken.
Work = 500 W x Time
Since the work done by the water pump is equal to the force multiplied by the distance, we can equate the two equations:
Force x Distance = Power x Time
20000 N x 15 m = 500 W x Time
Now, let's solve for Time:
Time = (20000 N x 15 m) / 500 W
Time = (300000 N m) / 500 W
Time = 600 s
Hence, the time taken by the water pump to lift the 2000 kg of water to a height of 15 m is 600 seconds.