Question

A. In the building there are 133 steps from the ground floor to the sixth floor.

Each step is 16.2 cm tall. It takes 6 minutes and 16 seconds for a person with a mass of m = 89.2 kg to walk all the way up. How much work did the person do?


b. What was the average power performed by the person during the walk?


c. How many food Calories did the person burn during the walk? (1 Cal = 4.1868 kJ. Do not enter unit for this part.)

Answer 1

(a)
`W\approx18834.7 \ J`

(b)
`P \approx 50.1 \ W`

(c)
`\text{Food Calories} \approx 4.5 \ cal}`

Step-by-step explanation:

Part (a): To calculate the work done by the person, we can use the formula:

`\rightarrow W= F d`

The force can be calculated using the person's mass and the acceleration due to gravity:

`\rightarrow F=mg`

Given:

Number of steps, N = 133

Height of each step, h = 16.2 cm = 0.162 m

Time taken to walk, t = 6 minutes and 16 seconds = 376 seconds

Mass of the person, m = 89.2 kg

First, let's calculate the vertical distance traveled:

`d=Nh\\\\\\\\\Longrightarrow d=(133)(0.162)\\\\\\\\\therefore d=21.546 \ m`

Now, we can calculate the work done:

`W= F d\\\\\\\\\Longrightarrow W=mgd\\\\\\\\\Longrightarrow W=(89.2)(9.8)(21.546)\\\\\\\\\therefore \boxed{\boxed{W\approx18834.7 \ J}}`

Therefore, the person did approximately 18,515.7 joules of work.

Part (b): The average power performed by the person can be calculated using the formula:

`\rightarrow P=(W)/(t)`

Calculating the average power by plugging in the appropriate values into the above formula:

`P=(W)/(t)\\\\\\\\\Longrightarrow P= (18834.7)/(376) \\\\\\\\\therefore \boxed{\boxed{P \approx 50.1 \ W}}`

Therefore, the average power performed by the person during the walk was approximately 50.1 watts.

Part (c): To calculate the food Calories burned during the walk, we need to convert the work done from joules to kilojoules (kJ) and then to food Calories:

`\rightarrow W \ \text{(in} \ kJ)=\frac{W \ \text{(in} \ J)}{1000}\\\\\\\\\Longrightarrow W \ \text{(in} \ kJ)=(18834.7)/(1000)\\\\\\\\\therefore W=18.8347 \ kJ`

`\rightarrow\text{Food Calories} = \frac{ W \ \text{(in} \ kJ)}{4.1868} \\\\\\\\\Longrightarrow \text{Food Calories} = ( 18.8347)/(4.1868)\\\\\\\\\therefore \boxed{\boxed{ \text{Food Calories} \approx 4.5 \ cal}}`

Therefore, the person burned approximately 4.5 food Calories during the walk.