A 145-lb student races up stairs with a vertical height of 4.8 m in 5.5 s to get to a class on the second floor. How much power in watts does the student expend in doing work against gravity
145lbs*1kg/2.2lbs=xxxxkg,figure that out.
power=work/time=massinKg*9.8N/kg*4.8m /5.5sec in joules...
To calculate the power expended by the student in doing work against gravity, we can use the formula:
Power (P) = Work (W) / Time (t)
First, let's calculate the work done by the student against gravity. The work done against gravity is equal to the force applied (the weight of the student) multiplied by the displacement (the vertical height the student climbed):
Work (W) = Force (F) x Displacement (d)
The weight of the student can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
Given that the mass of the student is 145 lbs, we need to convert this to kg:
Weight = 145 lbs x (1 kg / 2.2046 lbs) = 65.7709 kg
Acceleration due to gravity is approximately 9.8 m/s².
Weight = 65.7709 kg x 9.8 m/s² = 644.31162 N
Now, we can calculate the work done against gravity:
Work (W) = 644.31162 N x 4.8 m = 3095.396096 J (Joules)
Next, we plug this value of work into the power formula:
Power (P) = Work (W) / Time (t)
P = 3095.396096 J / 5.5 s ≈ 562.52638 W
Therefore, the student expends approximately 562.53 watts of power in doing work against gravity.
To calculate the power expended by the student to climb the stairs, we need to understand the concept of power and the formula used to calculate it.
Power is the rate at which work is done or the amount of energy transferred per unit time. It is calculated using the formula:
Power = Work / Time
In this case, the work done by the student against gravity is equal to the gravitational potential energy gained. The formula for gravitational potential energy is:
Potential Energy = mass x gravity x height
Where:
- mass is the student's weight converted to kilograms (1 lb = 0.4536 kg)
- gravity is the acceleration due to gravity (9.8 m/s^2)
- height is the vertical distance the student climbed
Let's calculate the power expended by the student to climb the stairs step by step:
Step 1: Convert the student's weight from pounds to kilograms:
mass = 145 lb * 0.4536 kg/lb = 65.7704 kg
Step 2: Calculate the potential energy:
Potential Energy = mass x gravity x height
Potential Energy = 65.7704 kg x 9.8 m/s^2 x 4.8 m = 3073.1712 Joules
Step 3: Calculate the power:
Power = Potential Energy / Time
Power = 3073.1712 J / 5.5 s = 558.5775 Watts
Therefore, the student expended approximately 558.58 Watts of power to climb the stairs.