A student in the fitness center lifts a weight with m = <81.5> kg from the floor to a height of <2.7> meters in a time of <15.50> seconds. Find the average power exerted by the student during this time. Give your answer in watts (W) and with 3 significant figures.
power in Watts = work in Joules per unit time
= m g h /t
= 81.5 * 9.81 * 2.70 / 15.50 Watts
By the way I do not believe it took the student 15.5 seconds to lift the weight. Do you have a typo?
To find the average power exerted by the student, we can use the formula:
Average Power = Work / Time
Work can be calculated using the formula:
Work = Force * Distance
The force exerted by the student can be calculated using the formula:
Force = mass * acceleration
In this case, since the weight is being lifted vertically, the acceleration can be assumed to be the acceleration due to gravity (g = 9.8 m/s^2). Therefore, the force exerted by the student can be calculated as:
Force = mass * acceleration = 81.5 kg * 9.8 m/s^2 = 799.7 N
The distance over which the weight is lifted is 2.7 meters.
Now we can calculate the work done by the student as:
Work = Force * Distance = 799.7 N * 2.7 m = 2159.19 J (to 3 significant figures).
Finally, we can calculate the average power as:
Average Power = Work / Time = 2159.19 J / 15.50 s = 139.3 W (to 3 significant figures).
Therefore, the average power exerted by the student during this time is approximately 139.3 watts.
To find the average power exerted by the student, we can use the formula:
Average Power = Work / Time
First, we need to calculate the work done by the student. The work is equal to the force applied multiplied by the distance over which it is applied.
Work = Force x Distance
The force applied by the student is equal to the weight of the weight lifted, which is given by the formula:
Force = mass x acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s^2.
So, we have:
Force = mass x acceleration due to gravity
Force = 81.5 kg x 9.8 m/s^2
Next, we calculate the distance over which the force is applied. The distance is the height through which the weight is lifted.
Distance = 2.7 m
Now, we can calculate the work done:
Work = Force x Distance
Work = (81.5 kg x 9.8 m/s^2) x 2.7 m
Finally, we can find the average power exerted by dividing the work done by the time taken:
Average Power = Work / Time
Average Power = ((81.5 kg x 9.8 m/s^2) x 2.7 m) / 15.50 s
Now we can calculate the average power exerted by the student.