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Questions and Answers
A box with a mass of 5 kg is lifted vertically 2 meters. By how much does the gravitational potential energy of the box change?
A box with a mass of 5 kg is lifted vertically 2 meters. By how much does the gravitational potential energy of the box change?
- Approximately 60 J
- Approximately 98 J (correct)
- Approximately 10 J
- Approximately 35 J
An object of mass $m$ moves with a velocity $v$. If the velocity is doubled, how does the kinetic energy of the object change?
An object of mass $m$ moves with a velocity $v$. If the velocity is doubled, how does the kinetic energy of the object change?
- Halves
- Remains the same
- Quadruples (correct)
- Doubles
A 2 kg ball is dropped from a height of 5 meters. Ignoring air resistance, what is the approximate kinetic energy of the ball just before it hits the ground?
A 2 kg ball is dropped from a height of 5 meters. Ignoring air resistance, what is the approximate kinetic energy of the ball just before it hits the ground?
- Approximately 49 J
- Approximately 25 J
- Approximately 98 J (correct)
- Approximately 196 J
A 1000 kg car accelerates from rest to a speed of 20 m/s over a distance of 80 m. What is the average net force acting on the car during this acceleration?
A 1000 kg car accelerates from rest to a speed of 20 m/s over a distance of 80 m. What is the average net force acting on the car during this acceleration?
A motor lifts a 20 kg object to a height of 10 meters in 5 seconds. What is the power supplied by the motor?
A motor lifts a 20 kg object to a height of 10 meters in 5 seconds. What is the power supplied by the motor?
Which of the following is true regarding the conservation of total mechanical energy (TME) of an object in motion under conservative forces?
Which of the following is true regarding the conservation of total mechanical energy (TME) of an object in motion under conservative forces?
If a simple pendulum is given an initial push, what effect does this have on the final angle compared to a pendulum released from rest?
If a simple pendulum is given an initial push, what effect does this have on the final angle compared to a pendulum released from rest?
How does increasing the length of a pendulum's string affect its period, assuming gravity remains constant?
How does increasing the length of a pendulum's string affect its period, assuming gravity remains constant?
A 0.5 kg ball attached to a string swings in a pendulum motion. At the lowest point, the ball's speed is 3 m/s. What is the kinetic energy of the ball at this point?
A 0.5 kg ball attached to a string swings in a pendulum motion. At the lowest point, the ball's speed is 3 m/s. What is the kinetic energy of the ball at this point?
For a pendulum, how will the total energy at the bottom of its swing compare to the total energy at its highest point, assuming energy is conserved and there is no initial push?
For a pendulum, how will the total energy at the bottom of its swing compare to the total energy at its highest point, assuming energy is conserved and there is no initial push?
Flashcards
Joule
Joule
SI unit of work or energy, equal to a Newton-meter (N·m) or kgm²/s².
Kinetic Energy
Kinetic Energy
Energy an object possesses due to its motion.
Potential Energy
Potential Energy
Energy stored in an object due to its position.
PE = mgh
PE = mgh
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KE = 1/2mv²
KE = 1/2mv²
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Power
Power
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Work-Energy Theorem
Work-Energy Theorem
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Total Mechanical Energy (TME)
Total Mechanical Energy (TME)
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Period of a Pendulum
Period of a Pendulum
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Pendulum
Pendulum
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Study Notes
- A joule is the standard unit of work or energy, equivalent to a Newton meter (N·m).
- A Newton equals kgm/s², so a joule also equals kgm²/s².
Kinetic Energy
- Kinetic energy refers to the energy an object has due to its motion
- KE = 1/2mv², where KE is kinetic energy in Joules (J), m is mass in kilograms (kg) and v is velocity in meters per second (m/s).
- Examples of kinetic energy include thermal energy, hydroelectric energy, and wind energy.
Potential Energy
- Potential energy is the energy stored in an object based on its position.
- PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above the ground.
- Chemical, gravitational, and nuclear energy are examples of potential energy.
- W = ΔΡΕ = PEp - PEi, where PE represents potential energy.
- fd = mghp - mghi; however this form is not very useful because you can factor out mg from the right side of the equation resulting in fd = mg(hp - h₁)
Power
- Power is the rate at which energy is changed or work is done, represented as P = W/t
- P = (mghp - mgh₁) / t.
- 1 horsepower (hp) is equivalent to 746 watts, while 1 kilowatt (kW) is 1000 watts.
Work-Energy Theorem
- The work done on an object by a net force equals the change in kinetic energy of the object
- W = ΔΚΕ = KEp - KEi.
- Since KE = ½mv², ΔΚΕ = ½mvp² - ½mvi².
- Therefore, f · d = ½mvp² - ½mvi².
- Work done at an angle is given by f · cosθ · d, which can be substituted into the work-energy theorem formula.
- Power is the rate at which energy changes or work is done, so P = W/t = (½mvp² - ½mvi²) / t.
Total Mechanical Energy
- Total Mechanical Energy (TME) is the energy an object has from its motion or stored position, represented as TME = KE + PE.
- TME remains constant throughout an object's path, though the distribution between potential and kinetic energy may vary.
- TMEi = TMEp, therefore KEi + PEi = KEp + PEp, and ½mvi² + mghi = ½mvp² + mghp.
Pendulums
- A pendulum involves a weight hung from a fixed point, swinging freely.
- The period (T) is the time for one complete swing (back and forth), depending only on the length of the string.
- T = 2π√(l/g, where l is the length of the string and g is the acceleration due to gravity (9.8 m/s²).
- If the mass is given an initial kinetic energy, the final angle will be larger than the initial angle (θi < θf).
- At the bottom there is no potential energy (all its energy must be kinetic).
- If trying to find the velocity at the bottom (vf), and there is no initial velocity and no final potential energy: g · h = ½ · vp², with h = l · (1 - cosθ), where θ is the angle.
- Simplified: √(2gh) = Vf.
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