Question

this is a multi - part item. as you saw in the simulation, the skaters total energy did not change. it was the sum of their potential and kinetic energies. this can be described mathematically according to the law of conservation of energy, where the total amount of energy in an isolated, closed system, $e_t$, remains conserved, or constant. while the amount of different types of energies may change, their total remains constant. mathematically, this means $e_t=pe + ke$ or $e_t=mgh+\frac{1}{2}mv^{2}$ for an object on the ramp. imagine a ball ($m = 0.250$ kg) is placed at rest ($v = 0$ m/s) at the top of the ramp ($h = 4.0$ m). assuming $g = 10.0$ m/s², how much energy in joules (j) does the marble have? enter your answer in the box. $e_t=square$ j

Explanation:

Step1: Identify kinetic and potential energy formulas

Potential energy $PE = mgh$, kinetic energy $KE=\frac{1}{2}mv^{2}$. The ball is at rest, so $KE = 0$.

Step2: Substitute values into potential - energy formula

Given $m = 0.250$ kg, $g=10.0$ m/s², $h = 4.0$ m. Then $PE=mgh=(0.250)\times(10.0)\times(4.0)$.

Step3: Calculate the potential energy

$PE=(0.250)\times(10.0)\times(4.0)=10$ J. Since $KE = 0$, the total energy $E_T=PE + KE=10$ J.

Answer:

10