each step of a ladder increases one's vertical height 40.0cm. If a 90 kg painter climbs 8 steps of the ladder, what is the increase in potential energy?
m g h
8 * .4 = 3.2 meters up
90 * 9.81 * 3.2 Joules
2,822.4
To calculate the increase in potential energy, we need to determine the change in height and multiply it by the weight and the acceleration due to gravity.
Given that each step of the ladder increases vertical height by 40.0 cm, the total change in height when climbing 8 steps can be calculated as:
Change in height = 40.0 cm/step * 8 steps = 320.0 cm
Since the unit of height is cm and the weight is given in kg, we need to convert the change in height to meters (m) and the weight to Newtons (N).
1 m = 100 cm, so the change in height is 320.0 cm * (1 m/100 cm) = 3.20 m
The weight of the painter is given as 90 kg. To convert it to Newtons, we multiply it by the acceleration due to gravity, which is approximately 9.8 m/s^2:
Weight in Newtons = 90 kg * 9.8 m/s^2 = 882 N
Finally, we can calculate the increase in potential energy using the formula:
Potential energy = Weight * Change in height
Potential energy = 882 N * 3.20 m = 2,822.4 Joules
Therefore, the increase in potential energy for the painter climbing 8 steps of the ladder is 2,822.4 Joules.
To calculate the increase in potential energy, we need to use the formula:
Potential energy (PE) = mass (m) × gravitational acceleration (g) × height (h)
In this case, the increase in height is obtained by multiplying the number of steps climbed by the vertical height increment of each step. Since each step increases the vertical height by 40.0 cm, and the painter climbed 8 steps, the total increase in height is:
Increase in height (h) = 40.0 cm/step × 8 steps
Now we can calculate the potential energy increase. The gravitational acceleration (g) is approximately 9.8 m/s², and the mass (m) of the painter is given as 90 kg (kilograms). However, we need to convert the increase in height from centimeters to meters:
Increase in height (h) = (40.0 cm/step × 8 steps) ÷ 100 cm/meter
Now we can substitute the values into the formula and calculate the increase in potential energy:
Potential energy increase = 90 kg × 9.8 m/s² × (40.0 cm/step × 8 steps) ÷ 100 cm/meter
Simplifying the calculation will give us the final answer.