Energy - practice problems
In mathematics and physics education, energy represents the capacity to do work or cause change, measured in joules. Key forms include kinetic energy (KE = ½mv²), potential energy (PE = mgh), and thermal energy. The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. Mathematical problems involving energy often require understanding quadratic relationships, systems of equations, and calculus for changing rates. Energy calculations appear in mechanics, thermodynamics, electricity, and chemistry. Students learn to apply formulas, convert between energy units, and analyze energy transformations in physical systems.Number of problems found: 207
- An electricity
If the Rodriguez family used 520 kilowatt-hours of electricity in 12 days, how many kilowatt-hours should they use in 6 days at the same usage rate? - Heat energy
Energy is measured using the unit Joule (J). Temperature is measured using the unit degree Celsius °C). To increase the temperature of 1 liter of water by 1 °C, 4200 J of heat energy is required. (a) Kelly wants to increase the temperature of 2 liters of - Electrical 11
An electrical device produces 4.2 MJ of work per hour at an efficiency of 53%. What is the power input of this device? - Rotational motion of a cylinder
Calculate the kinetic energy of a cylindrical body with radius r = 0.08 m and mass m = 1.5 kg at time t = 5 s, given that the body rotates about an axis through the centre of the cylinder with a constant angular acceleration ε = 5 rad/s², starting from re - Water + temperature
We supplied 1,365 kJ of heat to 5 kg of water initially at 20 °C. To what temperature did it heat up? - Heating water
5 kg of water warmed up by 10 °C. How much heat did the water absorb? (Remember that 1 kg of water requires 4,200 J of heat to raise its temperature by 1 °C.) - Heating 2
The heating element of a stove has an electrical resistance of 80 ohms and is connected to a voltage of 230 V. Calculate the electrical energy consumed in a year (365 days) if it is switched on for 2 hours a day. How much will the energy consumed cost if - Spiral - iron
An electric iron is connected to a 230 V power source. Its heating element has an electrical resistance of 100 ohms. Calculate the power of the iron and the electric current flowing through the element. - Aluminum ignote
At what temperature did the temperature stabilise if an aluminium ingot weighing 45 kg, initially at 15 °C, received 4.8 MJ of heat? The specific heat capacity of aluminium is 896 J/(kg·°C). - Capacity of iron
What was the initial temperature of an iron object weighing 30 kg that absorbed 3.5 kJ of heat when heated to 39 °C? The specific heat capacity of iron is 450 J/(kg·°C). - Calorimetric equation
A 200 g aluminium cylinder at 180 °C was dropped into 3 kg of water at 25 °C. At what temperature did the mixture stabilise? The specific heat capacity of water is 4,200 J/(kg·°C) and of aluminium is 896 J/(kg·°C). - Specific heat
How much heat must be added to convert 25 kg of ice at −15 °C into water at 23 °C? The specific heat of fusion of ice is 333 kJ/kg. - By mass
How much heat must be supplied to completely melt 45 kg of potassium initially at 22.4 °C and bring it to a temperature of 98 °C? The specific heat of fusion is 25.5 kJ/kg, the melting point is 63.32 °C, and the specific heat capacity of potassium is 757. - Elevator efficiency
To what height will an elevator motor with a power of 25 kW and an efficiency of 48.6% transport a cabin weighing 445 kg with seven people (average mass 64 kg per person) in 54 seconds? - Motor efficiency
Calculate the power input of a motor operating at an efficiency of 58% that lifts an elevator car (weighing 390 kg) with twenty boxes (each weighing 25 kg) to a height of 85 m in 29 seconds. - Staircase - escalator
An escalator moves downward at a speed of 0.6 m/s at an angle of 45° to the horizontal. A person weighing 80 kg walks upward on it at a speed of 0.9 m/s. Determine the distance covered by the person and the work done by him before he reaches a height of 2 - Soap bubble
A conductive soap bubble with a radius of r=2 cm and charged to a potential of φ= 10000 V will burst into a drop of water with a radius of r1= 0.05 cm. What is the potential φ1 of the drop? - Heat for Phase Change
How much heat is needed to turn 1 kg of ice at a temperature of -10℃ into steam at a temperature of 100℃? - Engine power Calculate the engine power of a truck moving at a constant speed of v= 30 km/h on a road with a 5% gradient when the weight of the truck with the load m= 5000 kg!
- Petra chair work
Petra pushed a chair from one room to another with a force of 60 N. She did 300 J of work. How far did Petra push the chair?
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