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?
h = 8steps * 0.4m/step = 3.2 m.
Ep = mg*h = 90kg*9.8N/kg * 3.2 = 2822.4 Joules.
To calculate the increase in potential energy, we need to multiply the weight of the painter by the vertical height gained.
Step 1: Determine the weight of the painter
The weight given is 90 kg, which is the mass of the painter. To find the weight, we need to multiply the mass by the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the painter is:
Weight = 90 kg × 9.8 m/s^2
Step 2: Calculate the vertical height gained
Each step of the ladder increases the vertical height by 40.0 cm. Since the painter climbs 8 steps, the total vertical height gained is:
Vertical Height Gained = 8 steps × 40.0 cm
Step 3: Convert the vertical height gained to meters
To maintain consistent units, we need to convert the vertical height gained from centimeters to meters. Since there are 100 centimeters in a meter, the vertical height gained in meters is:
Vertical Height Gained = (8 steps × 40.0 cm) / 100
Step 4: Calculate the increase in potential energy
Finally, we can calculate the increase in potential energy by multiplying the weight of the painter by the vertical height gained. Remember to use the weight in newtons and the vertical height in meters:
Increase in Potential Energy = Weight × Vertical Height Gained
By following these steps, you can calculate the increase in potential energy for the given scenario.