Energy

Gravitational potential energy is stored because the cyclist-bicycle system has a certain mass (m) and is at a certain height (h) above a reference point (usually the ground). The higher the object, the greater its gravitational potential energy, as defined by the equation GPE = mgh, where g is the acceleration due to gravity.

Work Done = Force x Distance
Work Done = 60 N x 12 m
Work Done = 720 J

Energy Transfer: Chemical energy stored in the cyclist's body is converted into kinetic energy of the bicycle and thermal energy due to friction in the moving parts. Some energy is also transferred as sound.

Electrical energy from the power source is transferred to the loudspeaker. Inside the loudspeaker, the electrical energy is converted primarily into sound energy, which travels as a wave through the air. Some electrical energy is also converted to thermal energy due to the resistance of the wires inside the speaker.

1. Calculate the initial potential energy (PE):
PE = mgh = 60 kg * 10 m/s² * 3.0 m = 1800 J

2. Calculate the final kinetic energy (KE):
KE = 0.5 * mv² = 0.5 * 60 kg * (7.0 m/s)² = 1470 J

3. Calculate the energy lost due to friction:
Energy Lost = PE - KE = 1800 J - 1470 J = 330 J

Answer: 330 J. This lost energy is converted into heat and sound due to the friction between the student and the slide, representing a transformation of energy while the total energy is conserved.

As the toy car rolls down the ramp:
1. Gravitational potential energy (GPE) decreases as the height decreases.
2. Kinetic energy (KE) increases as the car gains speed.
3. Some of the initial GPE is transformed into KE.
4. Due to friction between the wheels and the ramp (and air resistance), some of the initial GPE is also converted into heat and sound.

Total energy remains constant. The initial GPE is equal to the sum of the final KE and the energy dissipated as heat and sound. Energy is transformed, not created or destroyed.

Ek = (1/2) * m * v²
Ek = (1/2) * 0.45 kg * (16 m/s)²
Ek = (1/2) * 0.45 kg * 256 m²/s²
Ek = 57.6 J

The kinetic energy is calculated using the formula Ek = 1/2 mv², substituting the mass and velocity and calculating the final value.

The kinetic energy would double.

Explanation: Since kinetic energy (Ek) is directly proportional to mass (m) as seen in the equation Ek = (1/2)mv², if the mass doubles while the velocity (v) remains constant, the kinetic energy will also double.

ΔΕ = mgΔh
ΔΕ = (2.0 kg) x (9.8 N/kg) x (1.5 m)
ΔΕ = 29.4 J

The change in gravitational potential energy is the product of the mass, gravitational field strength, and the change in height.

As the ball rises, its height (Δh) increases. Since ΔΕ = mgΔh, and mass (m) and gravitational field strength (g) remain constant, the gravitational potential energy (ΔΕ) increases as the ball gains height. This is because work is being done against gravity, storing energy in the form of GPE.

Formula: Useful Energy Output = mgh; Efficiency = (Useful Energy Output / Total Energy Input) x 100

Working:
Useful Energy Output = (2.0 kg) * (9.81 m/s²) * (0.5 m) = 9.81 J
60% = (9.81 J / Total Energy Input) x 100
Total Energy Input = (9.81 J / 60) * 100 = 16.35 J

Answer: 16.35 J

Explanation: First, calculate the gravitational potential energy gained by the mass (useful energy). Then, use the efficiency formula to find the total electrical energy supplied to the motor. This accounts for energy losses due to heat and sound.

Explanation: The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In a filament lamp, not all the electrical energy is converted into light energy. A significant portion of the electrical energy is converted into heat energy, which is then dissipated into the surroundings. This heat is an unwanted form of energy transfer, reducing the amount of energy available as light, thus reducing the efficiency of the bulb. Other minor losses include infrared radiation.