A spray pump is used to spray water from a pool to a fountain
I) determine the power of the pump when the work done by the pump is 80Nm at 50m/s to a distance of 20m
ii) determine the mass of the pump when the water is projected at acceleration of 10m/s
To determine the power of the pump, we need to use the formula for work and power.
I) The formula for work is given by:
Work = Force x Distance
In this case, the work done by the pump is given as 80 Nm (Newton-meter), and the distance is 20 m.
Therefore, we can rearrange the formula to solve for force:
Force = Work / Distance
Force = 80 Nm / 20 m = 4 N
Now, we need to calculate the power. The formula for power is:
Power = Work / Time
However, we are not given the time in this case. But we can calculate the time using the given information about the speed.
Speed = Distance / Time
Plugging in the values, we have:
50 m/s = 20 m / Time
Rearranging the formula to solve for time:
Time = Distance / Speed
Time = 20 m / 50 m/s = 0.4 seconds
Now, we can calculate the power:
Power = Work / Time
Power = 80 Nm / 0.4 s = 200 Watts
Therefore, the power of the pump is 200 Watts.
ii) To determine the mass of the pump when the water is projected at an acceleration of 10 m/s^2, we can use Newton's second law of motion.
Force = Mass x Acceleration
In this case, the force is the force exerted by the pump (which we found to be 4 N), and the acceleration is given as 10 m/s^2.
So we can rearrange the formula to solve for mass:
Mass = Force / Acceleration
Mass = 4 N / 10 m/s^2 = 0.4 kg
Therefore, the mass of the pump is 0.4 kg.