The work done by a 75.0-kg person climbing stairs and gaining 2.50 meters in height, neglecting friction, is calculated to be 1837.5 joules, using the formula Work = Force × Distance with the force being the product of the person's weight and gravity.
Work Done by a Person Climbing Stairs
To calculate the work done by the person climbing the stairs, we use the formula for work in physics:
Work = Force × Distance
The force exerted is equal to the person's weight, which is the product of their mass and the acceleration due to gravity (9.8 m/s2). We assume gravity is the only force acting on the person in the vertical direction. Hence, the force (which in this case is the weight) will be:
Force = Mass × Gravity = 75.0 kg × 9.8 m/s2
This gives a force of 735 N (newtons). As the person gains a height of 2.50 meters while climbing the stairs, the work done can be calculated as:
Work = 735 N × 2.50 m = 1837.5 J (joules)
Therefore, the work done by the person to climb the stairs and gain a height of 2.50 meters is 1837.5 joules.