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Answer: Energy is the property that must be transferred to an object to perform work on it or to heat it up. The standard unit of energy is the joule (J).
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Answer: Four types of energy stores include:
- Kinetic store: A moving car
- Gravitational potential store: A book on a high shelf
- Chemical store: Food, batteries, fuel
- Thermal store: Hot water
Other valid examples include elastic potential store (stretched spring) and magnetic store (electromagnet).
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Answer: An energy store is a system that contains energy (like a moving object having kinetic energy or a battery having chemical energy). An energy transfer pathway is the way that energy moves from one store to another (like mechanical transfer through forces, electrical transfer through current, heating transfer due to temperature difference, or radiation transfer through waves).
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Answer: When a student uses a battery-powered calculator:
- Chemical energy stored in the battery is transferred through electrical pathways (as current flows through the calculator’s circuits)
- Some of this energy is transferred to light energy in the display
- Eventually, all energy is transferred to the thermal energy store of the surroundings as heat
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Answer:
Given:
- Mass (m) = 0.5 kg
- Height (h) = 20 m
- Gravitational field strength (g) = 9.8 N/kg
Using the formula for gravitational potential energy:
GPE = m × g × h
GPE = 0.5 × 9.8 × 20
GPE = 98 J
The gravitational potential energy of the ball before it is dropped is 98 joules.
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Answer:
Given:
- Mass (m) = 1500 kg
- Velocity (v) = 20 m/s
Using the formula for kinetic energy:
KE = ½ × m × v²
KE = ½ × 1500 × 20²
KE = 750 × 400
KE = 300,000 J
KE = 300 kJ
The kinetic energy of the car is 300 kilojoules.
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Answer: Kinetic energy is calculated using the formula KE = ½ × m × v². Since velocity is squared in this formula, doubling the speed means the velocity term is squared to 4 times its original value. Therefore, when speed doubles, kinetic energy quadruples (increases by a factor of 4).
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Answer:
Given:
- Mass (m) = 25 kg
- Height (h) = 1.8 m
- Gravitational field strength (g) = 9.8 N/kg
Using the formula for gravitational potential energy:
GPE = m × g × h
GPE = 25 × 9.8 × 1.8
GPE = 441 J
The box gains 441 joules of gravitational potential energy.
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Answer:
Given:
- Mass (m) = 80 kg
- Velocity (v) = 5 m/s
Using the formula for kinetic energy:
KE = ½ × m × v²
KE = ½ × 80 × 5²
KE = 40 × 25
KE = 1000 J
KE = 1 kJ
The kinetic energy of the cyclist and bicycle is 1000 joules or 1 kilojoule.
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Answer: When a pendulum swings:
- At the highest point, the energy is stored as gravitational potential energy
- As it swings downward, gravitational potential energy is transferred to kinetic energy
- At the lowest point, the energy is stored as kinetic energy (maximum velocity)
- As it swings upward, kinetic energy is transferred back to gravitational potential energy
- This energy transfer cycle continues, with some energy being transferred to thermal energy of the surroundings due to air resistance and friction, causing the pendulum to eventually stop
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Answer:
Given:
- Mass (m) = 60 kg
- Height (h) = 3 m
- Time (t) = 4 s
- Gravitational field strength (g) = 9.8 N/kg
a) Gravitational potential energy gained:
GPE = m × g × h
GPE = 60 × 9.8 × 3
GPE = 1764 J
b) Power developed:
Power = Energy ÷ Time
Power = 1764 ÷ 4
Power = 441 watts (W)
The athlete gains 1764 J of gravitational potential energy and develops 441 watts of power.
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Answer:
Given:
- Mass (m) = 0.2 kg
- Initial velocity (v) = 15 m/s
- Gravitational field strength (g) = 9.8 N/kg
a) Initial kinetic energy:
KE = ½ × m × v²
KE = ½ × 0.2 × 15²
KE = 0.1 × 225
KE = 22.5 J
b) Maximum height:
Using the principle of energy conservation:
At maximum height, all initial kinetic energy is converted to gravitational potential energy.
Initial KE = Final GPE
22.5 = m × g × h
22.5 = 0.2 × 9.8 × h
22.5 = 1.96 × h
h = 22.5 ÷ 1.96
h = 11.48 m
The initial kinetic energy is 22.5 J and the maximum height reached is 11.48 m.
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Answer:
Given:
- Mass (m) = 500 kg
- Height (h) = 40 m
- Gravitational field strength (g) = 9.8 N/kg
Gravitational potential energy at the top:
GPE = m × g × h
GPE = 500 × 9.8 × 40
GPE = 196,000 J
At the bottom of the hill, if all gravitational potential energy is converted to kinetic energy:
KE = GPE
½ × m × v² = 196,000
½ × 500 × v² = 196,000
250 × v² = 196,000
v² = 196,000 ÷ 250
v² = 784
v = √784
v = 28 m/s
The gravitational potential energy at the top is 196,000 J and the theoretical maximum speed at the bottom is 28 m/s.
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Answer: In a light bulb, electrical energy is transferred to both light energy and thermal energy (heat). A light bulb is not 100% efficient because a significant portion of the electrical energy is transferred to thermal energy rather than light energy. In a typical incandescent bulb, about 95% of the energy is wasted as heat and only 5% is transferred to useful light energy. This is why light bulbs feel hot when they’ve been on for a while.
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Answer:
Given:
- Mass (m) = 0.3 kg
- Velocity (v) = 2 m/s
- Gravitational field strength (g) = 9.8 N/kg
a) Initial kinetic energy:
KE = ½ × m × v²
KE = ½ × 0.3 × 2²
KE = 0.15 × 4
KE = 0.6 J
b) Height reached on the slope:
Using the principle of energy conservation:
Initial KE = Final GPE
0.6 = m × g × h
0.6 = 0.3 × 9.8 × h
0.6 = 2.94 × h
h = 0.6 ÷ 2.94
h = 0.204 m
h ≈ 0.2 m or 20 cm
The initial kinetic energy is 0.6 J and the car will reach a height of approximately 0.2 meters (20 centimeters) on the slope.
Answers – Energy – 1
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