Translational Kinetic Energy - AP Physics 1
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What is the kinetic energy of a 2 kg object moving at 0 m/s?
What is the kinetic energy of a 2 kg object moving at 0 m/s?
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$KE = 0 \text{ J}$. Zero velocity results in zero kinetic energy.
$KE = 0 \text{ J}$. Zero velocity results in zero kinetic energy.
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What happens to kinetic energy if both mass and velocity are doubled?
What happens to kinetic energy if both mass and velocity are doubled?
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Increases by a factor of 8. Mass doubles ($\times 2$) and velocity squared doubles ($\times 4$): $2 \times 4 = 8$.
Increases by a factor of 8. Mass doubles ($\times 2$) and velocity squared doubles ($\times 4$): $2 \times 4 = 8$.
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State the relationship between kinetic energy and mass.
State the relationship between kinetic energy and mass.
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Directly proportional. Doubling mass doubles kinetic energy when velocity is constant.
Directly proportional. Doubling mass doubles kinetic energy when velocity is constant.
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If kinetic energy is 200 J and velocity is 4 m/s, find the mass.
If kinetic energy is 200 J and velocity is 4 m/s, find the mass.
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$m = 25 \text{ kg}$. $200 = \frac{1}{2}m(4^2)$, so $m = \frac{2(200)}{16} = 25$ kg.
$m = 25 \text{ kg}$. $200 = \frac{1}{2}m(4^2)$, so $m = \frac{2(200)}{16} = 25$ kg.
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State the formula for translational kinetic energy.
State the formula for translational kinetic energy.
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$KE = \frac{1}{2}mv^2$. Fundamental formula where kinetic energy equals half the product of mass and velocity squared.
$KE = \frac{1}{2}mv^2$. Fundamental formula where kinetic energy equals half the product of mass and velocity squared.
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What is the kinetic energy formula rearranged for velocity?
What is the kinetic energy formula rearranged for velocity?
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$v = \text{sqrt}(\frac{2KE}{m})$. Solve $KE = \frac{1}{2}mv^2$ for $v$ by isolating the velocity term.
$v = \text{sqrt}(\frac{2KE}{m})$. Solve $KE = \frac{1}{2}mv^2$ for $v$ by isolating the velocity term.
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Find kinetic energy: mass = 0.5 kg, velocity = 10 m/s.
Find kinetic energy: mass = 0.5 kg, velocity = 10 m/s.
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$KE = 25 \text{ J}$. $KE = \frac{1}{2}(0.5)(10^2) = \frac{1}{2}(0.5)(100) = 25$ J.
$KE = 25 \text{ J}$. $KE = \frac{1}{2}(0.5)(10^2) = \frac{1}{2}(0.5)(100) = 25$ J.
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What does $v$ represent in the translational kinetic energy formula?
What does $v$ represent in the translational kinetic energy formula?
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Velocity of the object. Velocity is the vector quantity representing the object's speed and direction.
Velocity of the object. Velocity is the vector quantity representing the object's speed and direction.
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If mass is tripled and velocity is constant, how does $KE$ change?
If mass is tripled and velocity is constant, how does $KE$ change?
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Triples. Kinetic energy scales linearly with mass when velocity is constant.
Triples. Kinetic energy scales linearly with mass when velocity is constant.
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If velocity remains constant, how does kinetic energy change as mass increases?
If velocity remains constant, how does kinetic energy change as mass increases?
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Increases linearly. Direct proportional relationship when velocity remains constant.
Increases linearly. Direct proportional relationship when velocity remains constant.
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If mass is halved, how does kinetic energy change?
If mass is halved, how does kinetic energy change?
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Halved. Kinetic energy is directly proportional to mass.
Halved. Kinetic energy is directly proportional to mass.
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A 10 kg object moves at 0 m/s. What is its kinetic energy?
A 10 kg object moves at 0 m/s. What is its kinetic energy?
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$KE = 0 \text{ J}$. Zero velocity means zero kinetic energy regardless of mass.
$KE = 0 \text{ J}$. Zero velocity means zero kinetic energy regardless of mass.
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Calculate velocity: kinetic energy = 18 J, mass = 2 kg.
Calculate velocity: kinetic energy = 18 J, mass = 2 kg.
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$v = 3 \text{ m/s}$. $18 = \frac{1}{2}(2)v^2$, so $v = \sqrt{\frac{36}{2}} = 3$ m/s.
$v = 3 \text{ m/s}$. $18 = \frac{1}{2}(2)v^2$, so $v = \sqrt{\frac{36}{2}} = 3$ m/s.
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Identify the SI unit for velocity in the kinetic energy formula.
Identify the SI unit for velocity in the kinetic energy formula.
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Meters per second (m/s). SI derived unit combining distance per unit time.
Meters per second (m/s). SI derived unit combining distance per unit time.
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What does $m$ represent in the translational kinetic energy formula?
What does $m$ represent in the translational kinetic energy formula?
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Mass of the object. Mass is the scalar quantity representing the amount of matter in the object.
Mass of the object. Mass is the scalar quantity representing the amount of matter in the object.
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What are the SI units of translational kinetic energy?
What are the SI units of translational kinetic energy?
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Joules (J). Energy units derived from $kg \cdot m^2/s^2$ in the SI system.
Joules (J). Energy units derived from $kg \cdot m^2/s^2$ in the SI system.
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How is translational kinetic energy related to work done?
How is translational kinetic energy related to work done?
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Equal to work done to bring object to current speed. Work-energy theorem states work done equals change in kinetic energy.
Equal to work done to bring object to current speed. Work-energy theorem states work done equals change in kinetic energy.
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Convert 100 J to kilojoules (kJ).
Convert 100 J to kilojoules (kJ).
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$0.1 \text{ kJ}$. Divide by 1000 to convert joules to kilojoules.
$0.1 \text{ kJ}$. Divide by 1000 to convert joules to kilojoules.
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Identify the SI unit for mass used in the kinetic energy formula.
Identify the SI unit for mass used in the kinetic energy formula.
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Kilogram (kg). Standard SI base unit for measuring the amount of matter.
Kilogram (kg). Standard SI base unit for measuring the amount of matter.
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If velocity is doubled, how does kinetic energy change?
If velocity is doubled, how does kinetic energy change?
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Increases by a factor of 4. Since $v^2$ appears in the formula, doubling $v$ increases $KE$ by $2^2 = 4$.
Increases by a factor of 4. Since $v^2$ appears in the formula, doubling $v$ increases $KE$ by $2^2 = 4$.
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Calculate the kinetic energy: mass = 4 kg, velocity = 5 m/s.
Calculate the kinetic energy: mass = 4 kg, velocity = 5 m/s.
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$KE = 50 \text{ J}$. $KE = \frac{1}{2}(4)(5^2) = \frac{1}{2}(4)(25) = 50$ J.
$KE = 50 \text{ J}$. $KE = \frac{1}{2}(4)(5^2) = \frac{1}{2}(4)(25) = 50$ J.
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Calculate the mass of an object with 50 J of kinetic energy moving at 5 m/s.
Calculate the mass of an object with 50 J of kinetic energy moving at 5 m/s.
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$m = 4 \text{ kg}$. $50 = \frac{1}{2}m(5^2)$, so $m = \frac{2(50)}{25} = 4$ kg.
$m = 4 \text{ kg}$. $50 = \frac{1}{2}m(5^2)$, so $m = \frac{2(50)}{25} = 4$ kg.
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A car increases speed from 10 m/s to 20 m/s. By what factor does its kinetic energy increase?
A car increases speed from 10 m/s to 20 m/s. By what factor does its kinetic energy increase?
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Increases by a factor of 4. Velocity doubles, so $KE$ increases by $(2)^2 = 4$ times.
Increases by a factor of 4. Velocity doubles, so $KE$ increases by $(2)^2 = 4$ times.
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What is the kinetic energy of a 3 kg object moving at 2 m/s?
What is the kinetic energy of a 3 kg object moving at 2 m/s?
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$KE = 6 \text{ J}$. $KE = \frac{1}{2}(3)(2^2) = \frac{1}{2}(3)(4) = 6$ J.
$KE = 6 \text{ J}$. $KE = \frac{1}{2}(3)(2^2) = \frac{1}{2}(3)(4) = 6$ J.
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A 0.5 kg object has 8 J of kinetic energy. What is its velocity?
A 0.5 kg object has 8 J of kinetic energy. What is its velocity?
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$v = 4 \text{ m/s}$. $8 = \frac{1}{2}(0.5)v^2$, so $v = \sqrt{\frac{16}{0.5}} = 4$ m/s.
$v = 4 \text{ m/s}$. $8 = \frac{1}{2}(0.5)v^2$, so $v = \sqrt{\frac{16}{0.5}} = 4$ m/s.
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What factor affects translational kinetic energy the most?
What factor affects translational kinetic energy the most?
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Velocity, as $v$ is squared. The squared term makes velocity changes more impactful than mass changes.
Velocity, as $v$ is squared. The squared term makes velocity changes more impactful than mass changes.
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What is the formula to find mass from kinetic energy and velocity?
What is the formula to find mass from kinetic energy and velocity?
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$m = \frac{2KE}{v^2}$. Rearrange $KE = \frac{1}{2}mv^2$ to solve for mass.
$m = \frac{2KE}{v^2}$. Rearrange $KE = \frac{1}{2}mv^2$ to solve for mass.
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Determine the kinetic energy change if velocity triples.
Determine the kinetic energy change if velocity triples.
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Increases by a factor of 9. Tripling velocity increases $KE$ by $(3)^2 = 9$ times.
Increases by a factor of 9. Tripling velocity increases $KE$ by $(3)^2 = 9$ times.
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A 1 kg object moves at 3 m/s. Find its kinetic energy.
A 1 kg object moves at 3 m/s. Find its kinetic energy.
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$KE = 4.5 \text{ J}$. $KE = \frac{1}{2}(1)(3^2) = \frac{1}{2}(1)(9) = 4.5$ J.
$KE = 4.5 \text{ J}$. $KE = \frac{1}{2}(1)(3^2) = \frac{1}{2}(1)(9) = 4.5$ J.
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A 6 kg object moving at 2 m/s. Calculate its kinetic energy.
A 6 kg object moving at 2 m/s. Calculate its kinetic energy.
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$KE = 12 \text{ J}$. $KE = \frac{1}{2}(6)(2^2) = \frac{1}{2}(6)(4) = 12$ J.
$KE = 12 \text{ J}$. $KE = \frac{1}{2}(6)(2^2) = \frac{1}{2}(6)(4) = 12$ J.
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