Translational Kinetic Energy - AP Physics C: Mechanics
Card 1 of 30
What is the relationship between kinetic energy and speed?
What is the relationship between kinetic energy and speed?
Tap to reveal answer
KE is proportional to $v^2$. Kinetic energy has quadratic dependence on velocity.
KE is proportional to $v^2$. Kinetic energy has quadratic dependence on velocity.
← Didn't Know|Knew It →
If kinetic energy is constant, what happens to mass if velocity increases?
If kinetic energy is constant, what happens to mass if velocity increases?
Tap to reveal answer
Mass decreases. If KE constant and $v$ increases, $m$ must decrease proportionally.
Mass decreases. If KE constant and $v$ increases, $m$ must decrease proportionally.
← Didn't Know|Knew It →
What is the kinetic energy change for a velocity change from $2 \text{ m/s}$ to $4 \text{ m/s}$?
What is the kinetic energy change for a velocity change from $2 \text{ m/s}$ to $4 \text{ m/s}$?
Tap to reveal answer
Increases by a factor of 4. Velocity doubles from 2 to 4, so KE increases fourfold.
Increases by a factor of 4. Velocity doubles from 2 to 4, so KE increases fourfold.
← Didn't Know|Knew It →
What happens to kinetic energy if velocity is constant?
What happens to kinetic energy if velocity is constant?
Tap to reveal answer
KE remains constant. Constant velocity means no change in kinetic energy.
KE remains constant. Constant velocity means no change in kinetic energy.
← Didn't Know|Knew It →
What is the kinetic energy of a $5 \text{ kg}$ object at $10 \text{ m/s}$?
What is the kinetic energy of a $5 \text{ kg}$ object at $10 \text{ m/s}$?
Tap to reveal answer
$KE = 250 \text{ J}$. Using $KE = \frac{1}{2}(5)(10^2) = \frac{1}{2}(5)(100) = 250$ J.
$KE = 250 \text{ J}$. Using $KE = \frac{1}{2}(5)(10^2) = \frac{1}{2}(5)(100) = 250$ J.
← Didn't Know|Knew It →
Express the kinetic energy formula using $F$, $d$, and $m$.
Express the kinetic energy formula using $F$, $d$, and $m$.
Tap to reveal answer
No direct formula; use $KE = \frac{1}{2}mv^2$. Must use velocity relationship; force and displacement alone insufficient.
No direct formula; use $KE = \frac{1}{2}mv^2$. Must use velocity relationship; force and displacement alone insufficient.
← Didn't Know|Knew It →
What is the formula for translational kinetic energy?
What is the formula for translational kinetic energy?
Tap to reveal answer
$KE = \frac{1}{2}mv^2$. Standard formula where energy equals half mass times velocity squared.
$KE = \frac{1}{2}mv^2$. Standard formula where energy equals half mass times velocity squared.
← Didn't Know|Knew It →
Identify the unit of kinetic energy in the SI system.
Identify the unit of kinetic energy in the SI system.
Tap to reveal answer
Joule (J). Energy unit in metric system, equivalent to newton-meter.
Joule (J). Energy unit in metric system, equivalent to newton-meter.
← Didn't Know|Knew It →
What variable represents mass in the kinetic energy formula?
What variable represents mass in the kinetic energy formula?
Tap to reveal answer
$m$. Mass is the scalar quantity representing object's inertia.
$m$. Mass is the scalar quantity representing object's inertia.
← Didn't Know|Knew It →
What variable represents velocity in the kinetic energy formula?
What variable represents velocity in the kinetic energy formula?
Tap to reveal answer
$v$. Velocity is the vector quantity representing speed and direction.
$v$. Velocity is the vector quantity representing speed and direction.
← Didn't Know|Knew It →
Calculate the kinetic energy: $m = 2 \text{ kg}$, $v = 3 \text{ m/s}$.
Calculate the kinetic energy: $m = 2 \text{ kg}$, $v = 3 \text{ m/s}$.
Tap to reveal answer
$KE = 9 \text{ J}$. Using $KE = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9$ J.
$KE = 9 \text{ J}$. Using $KE = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9$ J.
← Didn't Know|Knew It →
What is the kinetic energy when $m = 0 \text{ kg}$?
What is the kinetic energy when $m = 0 \text{ kg}$?
Tap to reveal answer
$KE = 0 \text{ J}$. Zero mass means no kinetic energy regardless of velocity.
$KE = 0 \text{ J}$. Zero mass means no kinetic energy regardless of velocity.
← Didn't Know|Knew It →
How does kinetic energy change if velocity doubles?
How does kinetic energy change if velocity doubles?
Tap to reveal answer
Increases by a factor of 4. KE varies with $v^2$, so doubling velocity quadruples energy.
Increases by a factor of 4. KE varies with $v^2$, so doubling velocity quadruples energy.
← Didn't Know|Knew It →
What is the kinetic energy when $v = 0 \text{ m/s}$?
What is the kinetic energy when $v = 0 \text{ m/s}$?
Tap to reveal answer
$KE = 0 \text{ J}$. Zero velocity means object is at rest, no kinetic energy.
$KE = 0 \text{ J}$. Zero velocity means object is at rest, no kinetic energy.
← Didn't Know|Knew It →
What is the formula for translational kinetic energy?
What is the formula for translational kinetic energy?
Tap to reveal answer
$KE = \frac{1}{2}mv^2$. Standard formula where energy equals half mass times velocity squared.
$KE = \frac{1}{2}mv^2$. Standard formula where energy equals half mass times velocity squared.
← Didn't Know|Knew It →
Calculate $p$: $KE = 20 \text{ J}$, $m = 4 \text{ kg}$.
Calculate $p$: $KE = 20 \text{ J}$, $m = 4 \text{ kg}$.
Tap to reveal answer
$p = 8.94 \text{ kg m/s}$. Using $p = \sqrt{2mKE} = \sqrt{2(4)(20)} = \sqrt{160} ≈ 8.94$ kg⋅m/s.
$p = 8.94 \text{ kg m/s}$. Using $p = \sqrt{2mKE} = \sqrt{2(4)(20)} = \sqrt{160} ≈ 8.94$ kg⋅m/s.
← Didn't Know|Knew It →
Calculate the velocity: $KE = 36 \text{ J}$, $m = 4 \text{ kg}$.
Calculate the velocity: $KE = 36 \text{ J}$, $m = 4 \text{ kg}$.
Tap to reveal answer
$v = 4.24 \text{ m/s}$. Solving $36 = \frac{1}{2}(4)v^2$ gives $v = \sqrt{18} ≈ 4.24$ m/s.
$v = 4.24 \text{ m/s}$. Solving $36 = \frac{1}{2}(4)v^2$ gives $v = \sqrt{18} ≈ 4.24$ m/s.
← Didn't Know|Knew It →
What happens to kinetic energy if velocity is constant?
What happens to kinetic energy if velocity is constant?
Tap to reveal answer
KE remains constant. Constant velocity means no change in kinetic energy.
KE remains constant. Constant velocity means no change in kinetic energy.
← Didn't Know|Knew It →
How does kinetic energy change if velocity doubles?
How does kinetic energy change if velocity doubles?
Tap to reveal answer
Increases by a factor of 4. KE varies with $v^2$, so doubling velocity quadruples energy.
Increases by a factor of 4. KE varies with $v^2$, so doubling velocity quadruples energy.
← Didn't Know|Knew It →
How does kinetic energy change if mass is halved?
How does kinetic energy change if mass is halved?
Tap to reveal answer
Halves. KE is directly proportional to mass.
Halves. KE is directly proportional to mass.
← Didn't Know|Knew It →
Determine the velocity: $KE = 50 \text{ J}$, $m = 5 \text{ kg}$.
Determine the velocity: $KE = 50 \text{ J}$, $m = 5 \text{ kg}$.
Tap to reveal answer
$v = 4.47 \text{ m/s}$. Solving $50 = \frac{1}{2}(5)v^2$ gives $v = \sqrt{20} ≈ 4.47$ m/s.
$v = 4.47 \text{ m/s}$. Solving $50 = \frac{1}{2}(5)v^2$ gives $v = \sqrt{20} ≈ 4.47$ m/s.
← Didn't Know|Knew It →
Calculate kinetic energy: $m = 8 \text{ kg}$, $v = 7 \text{ m/s}$.
Calculate kinetic energy: $m = 8 \text{ kg}$, $v = 7 \text{ m/s}$.
Tap to reveal answer
$KE = 196 \text{ J}$. Using $KE = \frac{1}{2}(8)(7^2) = \frac{1}{2}(8)(49) = 196$ J.
$KE = 196 \text{ J}$. Using $KE = \frac{1}{2}(8)(7^2) = \frac{1}{2}(8)(49) = 196$ J.
← Didn't Know|Knew It →
What is the kinetic energy when $v = 0 \text{ m/s}$?
What is the kinetic energy when $v = 0 \text{ m/s}$?
Tap to reveal answer
$KE = 0 \text{ J}$. Zero velocity means object is at rest, no kinetic energy.
$KE = 0 \text{ J}$. Zero velocity means object is at rest, no kinetic energy.
← Didn't Know|Knew It →
Express kinetic energy in terms of momentum $p$ and mass $m$.
Express kinetic energy in terms of momentum $p$ and mass $m$.
Tap to reveal answer
$KE = \frac{p^2}{2m}$. Derived from $p = mv$ and substituting into kinetic energy formula.
$KE = \frac{p^2}{2m}$. Derived from $p = mv$ and substituting into kinetic energy formula.
← Didn't Know|Knew It →
If an object's kinetic energy is zero, what can be said about its velocity?
If an object's kinetic energy is zero, what can be said about its velocity?
Tap to reveal answer
Velocity is zero. Zero kinetic energy requires zero velocity (assuming non-zero mass).
Velocity is zero. Zero kinetic energy requires zero velocity (assuming non-zero mass).
← Didn't Know|Knew It →
What is the kinetic energy of a $3 \text{ kg}$ object at $0 \text{ m/s}$?
What is the kinetic energy of a $3 \text{ kg}$ object at $0 \text{ m/s}$?
Tap to reveal answer
$KE = 0 \text{ J}$. Zero velocity means object has no kinetic energy.
$KE = 0 \text{ J}$. Zero velocity means object has no kinetic energy.
← Didn't Know|Knew It →
Calculate the mass: $KE = 18 \text{ J}$, $v = 3 \text{ m/s}$.
Calculate the mass: $KE = 18 \text{ J}$, $v = 3 \text{ m/s}$.
Tap to reveal answer
$m = 4 \text{ kg}$. Solving $18 = \frac{1}{2}m(3^2)$ gives $m = 4$ kg.
$m = 4 \text{ kg}$. Solving $18 = \frac{1}{2}m(3^2)$ gives $m = 4$ kg.
← Didn't Know|Knew It →
What is the kinetic energy change if velocity doubles?
What is the kinetic energy change if velocity doubles?
Tap to reveal answer
Increases by a factor of 4. KE varies with $v^2$, so doubling velocity quadruples energy.
Increases by a factor of 4. KE varies with $v^2$, so doubling velocity quadruples energy.
← Didn't Know|Knew It →
What is the kinetic energy of a $2 \text{ kg}$ object at $5 \text{ m/s}$?
What is the kinetic energy of a $2 \text{ kg}$ object at $5 \text{ m/s}$?
Tap to reveal answer
$KE = 25 \text{ J}$. Using $KE = \frac{1}{2}(2)(5^2) = \frac{1}{2}(2)(25) = 25$ J.
$KE = 25 \text{ J}$. Using $KE = \frac{1}{2}(2)(5^2) = \frac{1}{2}(2)(25) = 25$ J.
← Didn't Know|Knew It →
Calculate kinetic energy: $m = 6 \text{ kg}$, $v = 3 \text{ m/s}$.
Calculate kinetic energy: $m = 6 \text{ kg}$, $v = 3 \text{ m/s}$.
Tap to reveal answer
$KE = 27 \text{ J}$. Using $KE = \frac{1}{2}(6)(3^2) = \frac{1}{2}(6)(9) = 27$ J.
$KE = 27 \text{ J}$. Using $KE = \frac{1}{2}(6)(3^2) = \frac{1}{2}(6)(9) = 27$ J.
← Didn't Know|Knew It →