To determine the power needed to lift a 200 Newton object to a height of 4 meters in 4 seconds, we'll follow these steps:
1. Calculate the work done:
- Work (W) is defined as the product of the force (F) applied to an object and the distance (d) the object is moved in the direction of the force.
- Given:
- Force, [tex]\( F = 200 \)[/tex] Newtons
- Distance, [tex]\( d = 4 \)[/tex] meters
- The formula for work is:
[tex]\[
W = F \times d
\][/tex]
- Substituting the given values:
[tex]\[
W = 200 \text{ N} \times 4 \text{ m} = 800 \text{ Joules}
\][/tex]
2. Calculate the power needed:
- Power (P) is defined as the rate at which work is done, which is the work done divided by the time (t) it takes to do that work.
- Given:
- Time, [tex]\( t = 4 \)[/tex] seconds
- The formula for power is:
[tex]\[
P = \frac{W}{t}
\][/tex]
- Substituting the calculated work and the given time:
[tex]\[
P = \frac{800 \text{ Joules}}{4 \text{ seconds}} = 200 \text{ Watts}
\][/tex]
Therefore, the power needed to lift the 200 Newton object to a height of 4 meters in 4 seconds is 200 Watts.
