Question

a rocket traveling through space high above the ground has *
potential energy
kinetic energy
potential and kinetic energy
no potential of kinetic energy
a person does work if_ *
they sleep through school one day
they push a car stuck in the snow, but it doesnt move
they carry a baby across the room.
they lift a baby 1 meter off the floor
which of the following will increase the kinetic energy the most? *
triple the height
triple the velocity
triple the mass
they all result in the same change to the kinetic energy

Explanation:

First Question (Rocket Energy)

A rocket moving in space high above ground has speed (so kinetic energy, $KE = \frac{1}{2}mv^2$) and is at a height (so gravitational potential energy, $PE = mgh$). Thus, it has both.

Work is $W = Fd\cos\theta$. Sleeping (no force/displacement), pushing a non - moving car ($d = 0$), carrying a baby (force is vertical, displacement horizontal, $\cos90^{\circ}=0$). Lifting a baby 1m has force (equal to baby's weight) and displacement, so work is done.

Step1: Recall Kinetic Energy Formula

Kinetic Energy is given by the formula $KE=\frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity. Potential Energy related to height is $PE = mgh$, which is not kinetic energy.

Step2: Analyze Each Option

• Triple the height: This affects potential energy ($PE=mgh$), not kinetic energy. So this option does not increase kinetic energy.
• Triple the velocity: If the original velocity is $v$, the new velocity $v' = 3v$. The original $KE=\frac{1}{2}mv^{2}$, the new $KE'=\frac{1}{2}m(3v)^{2}=\frac{1}{2}m\times9v^{2}=9\times(\frac{1}{2}mv^{2}) = 9KE$.
• Triple the mass: If the original mass is $m$, the new mass $m' = 3m$. The original $KE=\frac{1}{2}mv^{2}$, the new $KE'=\frac{1}{2}(3m)v^{2}=3\times(\frac{1}{2}mv^{2})=3KE$.

Since tripling the velocity leads to a 9 - fold increase in KE, tripling the mass leads to a 3 - fold increase, and tripling the height does not affect KE, tripling the velocity increases KE the most.

Answer:

Potential and Kinetic Energy

Second Question (Work Done)