What is the cost of operating a 25 W light bulb 4.0 h a day for 6.0 days if the price of electrical
energy is 5¢/kWh? 9. A forklift uses 5200 J of energy to lift a 50.0 kg mass to a height of 4.0 m at a constant speed.
What is the efficiency of the forklift?
To calculate the cost of operating a light bulb, we need to determine the energy consumed by the bulb and then multiply it by the cost of electrical energy.
Step 1: Calculate the energy consumed by the light bulb.
Energy = Power x Time
Given:
Power of light bulb = 25 W
Time = 4.0 h/day x 6.0 days
First, convert the time from hours to kilowatt-hours (kWh):
Time = 4.0 h/day x 6.0 days = 24 h
Now, calculate the energy consumed:
Energy = Power x Time = 25 W x 24 h = 600 Wh = 0.6 kWh
Step 2: Calculate the cost of operating the light bulb.
Cost = Energy x Price of Electrical Energy
Given:
Price of electrical energy = 5¢/kWh
Now, calculate the cost:
Cost = 0.6 kWh x 5¢/kWh = 3¢
Therefore, the cost of operating the 25 W light bulb for 4.0 h a day for 6.0 days is 3¢.
Moving on to the second question:
To calculate the efficiency of the forklift, we need to compare the input energy (the energy supplied to the forklift) with the output energy (the energy used to lift the mass).
Efficiency = (Output Energy / Input Energy) x 100
Given:
Input Energy = 5200 J
Output Energy = Work done to lift the mass = Force x Distance
Given:
Mass = 50.0 kg
Height = 4.0 m
Speed = constant, implying no acceleration (which means no additional work is done apart from lifting the mass)
Force (F) = Weight = Mass x Gravity
Gravity ≈ 9.8 m/s^2 (acceleration due to gravity)
Force (F) = 50.0 kg x 9.8 m/s^2 = 490 N
Now, calculate the output energy (work done):
Output Energy (Work) = Force x Distance = 490 N x 4.0 m = 1960 J
Finally, calculate the efficiency:
Efficiency = (Output Energy / Input Energy) x 100
Efficiency = (1960 J / 5200 J) x 100
Simplifying,
Efficiency = (0.377) x 100 = 37.7%
Therefore, the efficiency of the forklift is 37.7%.