A 136-lb. student races up stairs with a vertical height of 4.8 m in 6.0 s to get to a class on the second floor. How much power in watts does the student expend in doing work against gravity?

Well, it seems like this student is really taking the "step" to success quite literally! Now, let's calculate the power they expend in climbing those stairs.

To find the power expended against gravity, we can use the formula:

Power (P) = Work (W) / Time (t)

Since the student is doing work against gravity, we need to calculate the work done first. The work done against gravity can be calculated using the formula:

Work (W) = Force (F) x Distance (d)

The force against gravity can be found using the formula:

Force (F) = mass (m) x gravitational acceleration (g)

So, to calculate the force against gravity, let's convert the student's weight from pounds to kilograms first. We can use the conversion factor of 1 lb = 0.4536 kg.

136 lb = 136 lb x 0.4536 kg/lb ≈ 61.69 kg

Now, let's calculate the force against gravity:

Force (F) = 61.69 kg x 9.8 m/s² ≈ 604.51 N

Next, we can calculate the work done against gravity:

Work (W) = Force (F) x Distance (d) = 604.51 N x 4.8 m ≈ 2903.57 J

Finally, we can calculate the power expended against gravity:

Power (P) = Work (W) / Time (t) = 2903.57 J / 6.0 s ≈ 483.93 W

So, the student is exerting approximately 483.93 watts of power to climb those stairs! That's quite an electric performance!

To find the power expended by the student in doing work against gravity, we can use the formula:

Power = Work / Time

First, we need to calculate the work done by the student against gravity. The work done against gravity is equal to the force exerted by the student multiplied by the distance moved vertically. The force exerted by the student against gravity is equal to the weight of the student.

Weight = mass * acceleration due to gravity

The weight of the student can be calculated using the formula:

Weight = mass * acceleration due to gravity

Given that the student weighs 136 lbs, we need to convert it to kg:

Weight (kg) = 136 lbs * 0.4536 kg/lb = 61.7 kg

Acceleration due to gravity is approximately 9.8 m/s^2.

So, the weight of the student is 61.7 kg * 9.8 m/s^2 = 604.46 N.

The work done against gravity is equal to the force multiplied by the distance moved vertically:

Work = Force * Distance

Given that the vertical height of the stairs is 4.8 m, the work done against gravity is:

Work = 604.46 N * 4.8 m = 2901.41 J

Now, we can calculate the power expended by the student by dividing the work done against gravity by the time taken:

Power = Work / Time

Given that the time taken is 6.0 s, the power expended by the student is:

Power = 2901.41 J / 6.0 s ≈ 483.6 W

Therefore, the student expends approximately 483.6 watts of power in doing work against gravity.

To calculate the power exerted by the student in climbing the stairs, we need to use the formula:

Power = Work / Time

First, we need to find the work done against gravity. The work done against gravity can be calculated using the formula:

Work = Force × Distance

In this case, the force is equal to the weight of the student, which is given as 136 lb. To convert this to Newtons, we need to multiply by the conversion factor: 1 lb = 4.448 N.

Weight = 136 lb × 4.448 N/lb
Weight = 604.928 N

Next, we need to calculate the distance, which is the vertical height of the stairs, given as 4.8 m.

Now we can calculate the work done against gravity:

Work = 604.928 N × 4.8 m
Work = 2903.7184 Joules

Finally, we can calculate the power:

Power = 2903.7184 Joules / 6.0 s
Power = 483.95 Watts

Therefore, the student expends approximately 483.95 watts of power in doing work against gravity.

power = work/time

work = force * distance

136 lb * 4.448N/lb = 605N
605N * 4.8m / 6.0s = 484W