1.A motor is rated at 1.5 hp. At what speed in m/s can this motor raise a 200 kg load?

2. A bucket of water with a total weight of 50 Newtons is lifted at constant
velocity up a 10 meter deep well. If it takes 20 seconds to raise the bucket
this distance, what is the power required to lift the bucket?​

1. 0.57 m/s

2. 25 Watts

Explanation:

1. Determination of the speed.

We'll begin by converting 1.5 hp to watt (W). This can be obtained as follow:

1 hp = 745.7 W

Therefore,

1.5 hp = 1.5 hp × 745.7 W / 1 hp

1.5 hp = 1118.55 W

Next, we shall determine the force. This can be obtained as follow:

Mass (m) = 200 Kg

Acceleration due to gravity (g) = 9.8 m/s²

Force (F) =?

F = m × g

F = 200 × 9.8

F = 1960 N

Finally, we shall determine the speed. This can be obtained as follow:

Power (P) = 1118.55 W

Force (F) = 1960 N

Speed (v) =?

P = F × v

1118.55 = 1960 × v

Divide both side by 1960

v = 1118.55 / 1960

v = 0.57 m/s

Thus, the speed is 0.57 m/s

2. Determination of the power.

We'll begin by calculating the velocity. This can be obtained as follow:

Displacement = 10 m up

Time = 20 s

Velocity =?

Velocity = Displacement / time

Velocity = 10 / 20

Velocity = 0.5 m/s

Finally, we shall determine the power. This can be obtained as follow:

Velocity (v) = 0.5 m/s

Force (F) = 50 N

Power (P) =?

P = F × v

P = 50 × 0.5

P = 25 Watts

Therefore, the power required to lift the bucket is 25 Watts

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