A man whose mass is 25kg ran up a flight of 25 steps each 20cm height how much work did they man do?.
25kg * 9.81N/kg * (25 * 0.20)m = ____ J
Well, let me put on my math clown hat for this one! If the man ran up a flight of 25 steps, each with a height of 20cm, we can calculate the work he did using the formula:
Work = Force × Displacement
Now, we know that work is equal to the force applied times the distance covered. In this case, the force is equal to the man's mass multiplied by the acceleration due to gravity (which is about 9.8 m/s²). The displacement is the total vertical height he climbed, which is 25 steps times 20cm (or 0.2m) per step.
So, the work done by the man is:
Work = (25kg × 9.8m/s²) × (25 steps × 0.2m/step)
Now, let's do some calculations here...
*beep boop beep*
And the answer is... drumroll, please...
Oh, wait, let's add some clown suspense...
*drrrrrrrr*
The man did approximately 1225 joules of work! That's a pretty energized workout!
To calculate the work done by the man, the following steps must be taken:
1. Determine the total vertical distance covered by the man while climbing the flight of stairs.
- Each step has a height of 20 cm, so the total vertical distance is calculated by multiplying the number of steps by the height of each step.
- In this case, there are 25 steps and each step is 20 cm high, so the total vertical distance covered is:
Total Vertical Distance = Number of Steps x Height of Each Step
= 25 steps x 20 cm
= 500 cm
2. Convert the total vertical distance from centimeters to meters to align with the standard unit of work (Joules).
- Since 1 meter is equal to 100 centimeters, divide the total vertical distance by 100 to convert it to meters.
- Total Vertical Distance (in meters) = Total Vertical Distance (in centimeters) ÷ 100
= 500 cm ÷ 100
= 5 meters
3. Calculate the work done by the man using the formula:
Work = Force x Distance
- The force required to overcome gravity is equal to the product of mass and acceleration due to gravity.
- The acceleration due to gravity is approximately 9.8 m/s².
- The distance traveled vertically is the total vertical distance covered by the man.
- Substituting the values into the formula:
Work = Mass x Acceleration due to Gravity x Vertical Distance
= 25 kg x 9.8 m/s² x 5 m
= 1225 J
Therefore, the man did 1225 Joules of work while running up the flight of stairs.
To calculate the work done by the man, we need to use the formula for work:
Work = Force × Distance
In this case, the force is equal to the weight of the man, which can be calculated using the formula:
Weight = mass × gravitational acceleration
The gravitational acceleration on Earth is approximately 9.8 m/s².
First, let's calculate the force exerted by the man:
Weight = 25 kg × 9.8 m/s² = 245 N
Now, we need to calculate the distance covered by the man. Since we know the height of each step (20 cm) and the number of steps (25), we can multiply the height by the number of steps to find the total distance covered:
Distance = height of each step × number of steps
Distance = 20 cm × 25 steps
However, we need to convert the height to meters to maintain consistent units:
Distance = (20 cm × 0.01 m/cm) × 25 steps
Now we can calculate the distance covered:
Distance = 0.2 m × 25 steps = 5 m
Finally, we can calculate the work done by the man:
Work = Force × Distance
Work = 245 N × 5 m
Work = 1225 Joules
Therefore, the man did 1225 Joules of work running up the flight of 25 steps.