How Do You Calculate Kinetic and Potential Energy in Free Fall?

[KTiaam]

Homework Statement

A mass m = 2 is in free fall. The acceleration of gravity is g = 10. All numbers are in mks units. The position y(t) and velocity v(t) of the mass as a function of time t are y(t)=9−5t2 and v(t)=−10t. Find each of the energies (K,U,E) as a function of time t. Hint: substitute v(t) into K(v), substitute y(t) into U(y).

Homework Equations

k = 1/2mv²
u = mgy

The Attempt at a Solution

I know that:
Work = ΔK
-ΔU = ΔK

im having trouble switching the equation to a function of time.
Am i trying to approach the problem in the wrong way?

any help is appreciated. Thanks!

 

[MuIotaTau]

Your formula for $U$ is a little off. (Hint: check your units!)

 

[KTiaam]

oh okay i solved the problem thank you!

 

[MuIotaTau]

Sure thing, happy to help!

 

[Nickie]

I would approach this problem by first understanding the concept of conservation of energy. Conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this problem, the mass is in free fall, which means that it is only experiencing gravitational potential energy and kinetic energy.

To solve for the energies as a function of time, we can use the equations for kinetic energy (K) and gravitational potential energy (U) as follows:

K = 1/2mv^2 = 1/2m(-10t)^2 = 50m(t)^2
U = mgy = m(10)(9-5t^2) = 90m - 50mt^2

Therefore, the total energy (E) can be calculated as:
E = K + U = 50m(t)^2 + 90m - 50mt^2 = 90m + 50m(t)^2

We can see that the energies are functions of time, as they both have the variable t in their equations. This means that as time changes, the values of K, U, and E will also change. We can also see that the mass (m) is a constant in all of the equations, so it does not change over time.

In summary, by understanding the concept of conservation of energy and using the equations for kinetic and potential energy, we can calculate the energies as functions of time in this problem.