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Considering the definition of work and power, the maximum height to which a 1200-watt motor could lift an object weighing 200 newtons in 4.0 seconds is 24 m.
Power is defined as how fast work is done. That is, power is the amount of work done per unit of time:
[tex]Power=\frac{work}{time}[/tex]
P is the power developed by the force that performs the work and its unit of measurement in the International System is Watts (W).
The unit of measurement of work in the International System is the Joule (J). The time during which the work is developed has the unit of measurement in the International System of seconds (s).
On the other side, work is defined as the force that is applied on a body to move it from one point to another.
When a net force is applied to the body or a system and this produces displacement, then that force is said to perform mechanical work. This work can be positive if the system gains energy or negative if the system loses energy.
The work is equal to the product of the force by the distance and by the cosine of the angle that exists between the direction of the force and the direction that travels the point or the object that moves.
In this case, the angle between the force and the displacement is 0 degrees. This is because the force and the displacement are in the same direction and sense, in the horizontal direction. So the cosine of 0 degrees will have a value of 1. Then work is equal to:
Work= force× distance
Then, the power can be calculated as:
[tex]Power=\frac{forcexdistance}{time}[/tex]
In this case, you know:
Replacing in the definition of power:
[tex]1200 W=\frac{200 Nxdistance}{4 s}[/tex]
Solving:
1200 W× 4 s= 200 N× distance
4800 W×s= 200 N× distance
4800 W×s ÷ 200 N= distance
24 m= distance
In summary, the maximum height to which a 1200-watt motor could lift an object weighing 200 newtons in 4.0 seconds is 24 m.
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