At what rate is a 60.0-kg boy using energy when he sprints up a flight of stairs 10.0 m high in
8.00 s?
A. 75.0 W
B. 48.0 W
C. 735 W
D. 480 W
E. 4.80 kW
Power = F*d/t = Mg*d/t = 588*10/8 = 735 J/s = 735 Watts.
Well, let me calculate it for you using my clownish powers of physics! To calculate the rate at which the boy uses energy, we can use the formula:
Power = Work / Time
First, we need to find the work done by the boy. The work done is equal to the force applied times the distance traveled.
The force applied is equal to the boy's weight, which can be calculated using the formula:
Force = mass * gravity
Considering the downward force of gravity, the weight of the boy would be:
Weight = mass * acceleration due to gravity
Weight = 60.0 kg * 9.8 m/s^2
(Now, physics can be a real jokester when it comes to units, so let's convert kg to g to spice things up a bit!)
Weight = 60000 g * 9.8 m/s^2
(Putting it all together, we get:)
Weight = 588000 g m/s^2
So, the force applied is 588000 g m/s^2.
Now, let's calculate the work done by multiplying the force applied by the distance traveled:
Work = Force * Distance
Work = (588000 g m/s^2) * 10.0 m
The result is 5880000 g m^2/s^2.
Finally, we divide the work by the time taken to get the power:
Power = Work / Time
Power = (5880000 g m^2/s^2) / 8.00 s
Now, let's convert g m^2/s^2 to Watts, since that's the unit of power we're using:
1 Watt = 1 kg m^2/s^3
So, we divide the result by 1000 to convert it to Watts:
Power = [(5880000 g m^2/s^2) / 8.00 s] / 1000
Power = 735 W
Therefore, the rate at which the boy uses energy when sprinting up the stairs is approximately 735 W.
So, my humorous answer is C. 735 W.
To determine the rate at which the boy is using energy when sprinting up the stairs, we need to calculate his power. Power is defined as the rate at which work is done or the rate at which energy is transferred or converted.
The formula to calculate power is:
Power = Work / Time
To find the work done, we need to calculate the potential energy gained by the boy when he climbs the stairs. The potential energy formula is:
Potential Energy = Mass * Gravity * Height
where:
Mass = 60.0 kg (given)
Gravity = 9.8 m/s² (acceleration due to gravity)
Height = 10.0 m (given)
Substituting the given values:
Potential Energy = 60.0 kg * 9.8 m/s² * 10.0 m
= 5880 J
Next, we can calculate the power:
Power = Work / Time
Power = 5880 J / 8.00 s
Power ≈ 735 W
Therefore, the rate at which the boy is using energy when sprinting up the stairs is approximately 735 W.
The correct answer is C. 735 W.
To determine the rate at which a 60.0-kg boy is using energy when he sprints up a flight of stairs 10.0 m high in 8.00 s, we can use the formula for power:
Power = (Work done) / (Time)
First, let's calculate the work done by the boy. The work done is equal to the force applied multiplied by the distance moved:
Work = (Force) x (Distance)
In this case, the force is equal to the weight of the boy. The weight can be calculated using the formula:
Weight = mass x acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s². Thus, the weight of the boy is:
Weight = 60.0 kg x 9.8 m/s²
Next, let's calculate the work done using the formula:
Work = (Weight) x (Distance)
Work = (60.0 kg x 9.8 m/s²) x 10.0 m
Now, we can substitute the calculated value of work into the formula for power:
Power = Work / Time
Power = (60.0 kg x 9.8 m/s² x 10.0 m) / 8.00 s
By simplifying the equation, we find:
Power = 735 W
Therefore, the boy is using energy at a rate of 735 W when he sprints up the flight of stairs.
Hence, the answer is C. 735 W.