During a workout, the football players at State U. ran up the stadium stairs in 61 s. The stairs are 145 m long and inclined at an angle of 30°. If a typical player has a mass of 105 kg, estimate the average power output on the way up. Ignore friction and air resistance.

power=work/time=145sin30*105g/61 watts

This was one of my labs, the lard butts in physics got some exercise and some calculations.

To estimate the average power output, we can use the equation for power:

Power = work / time

First, let's calculate the work done by the football players while running up the stadium stairs. Work is given by the equation:

Work = force x distance x cosine(angle)

The force exerted by the football player while running up the stairs can be calculated using Newton's second law of motion:

Force = mass x acceleration

Since the stairs are inclined at an angle of 30°, the vertical component of the acceleration can be calculated as:

Vertical acceleration = acceleration x sin(angle)

However, since there is no vertical displacement while running up the stairs, the vertical acceleration would be zero. So, the force exerted by the football player while running up the stairs is equal to the force due to gravity:

Force = mass x gravitational acceleration

Gravitational acceleration is approximately 9.8 m/s^2.

Now, let's calculate the work done:

Work = mass x gravitational acceleration x distance x cosine(angle)

Substituting the given values, we have:

Work = 105 kg x 9.8 m/s^2 x 145 m x cos(30°)

Next, we can calculate the average power output:

Power = Work / time

Substituting the given time of 61 s and the previously calculated work, we have:

Power = (105 kg x 9.8 m/s^2 x 145 m x cos(30°)) / 61 s

Calculating this expression will give us the average power output of the football players while running up the stadium stairs.

To estimate the average power output of a football player running up the stadium stairs, we need to calculate the work done and then divide it by the time taken.

1. Calculate the work done:
The work done is equal to the force applied multiplied by the distance traveled. In this case, the force can be calculated using the component of the player's weight perpendicular to the stairs, which is given by the equation:

Force = mass * gravity * sin(angle)

where mass is the mass of the player (105 kg), gravity is the acceleration due to gravity (9.8 m/s^2), and angle is the angle of inclination (30°).

Force = 105 kg * 9.8 m/s^2 * sin(30°)

2. Calculate the distance traveled:
The distance traveled is given as 145 m.

3. Calculate the work done:
Work = Force * distance

4. Calculate the average power output:
Power = Work / time

Given that the time taken is 61 seconds, we can substitute the values into the equation to calculate the average power output.

Now, let's perform the calculations:

Force = 105 kg * 9.8 m/s^2 * sin(30°) = 520.54 N

Work = 520.54 N * 145 m = 75,355.3 J

Power = 75,355.3 J / 61 s ≈ 1,234.75 W

Therefore, the average power output of the football player running up the stadium stairs can be estimated to be approximately 1,234.75 Watts.