calculating potential energy on the moon\nthe acceleration due to gravity on the moon is 1.6 m/s². what is…

calculating potential energy on the moon\nthe acceleration due to gravity on the moon is 1.6 m/s². what is the gravitational potential energy of a 1200 - kg lander resting on top of a 350 - m hill?\nj\nhow many times more gravitational potential energy would the same lander have on top of a 350 - m hill on earth?\nit would have times more gravitational potential energy.

calculating potential energy on the moon\nthe acceleration due to gravity on the moon is 1.6 m/s². what is the gravitational potential energy of a 1200 - kg lander resting on top of a 350 - m hill?\nj\nhow many times more gravitational potential energy would the same lander have on top of a 350 - m hill on earth?\nit would have times more gravitational potential energy.

Answer

Answer:

  1. First question: 672000
  2. Second question: 6.25

Explanation:

Step1: Recall gravitational - potential - energy formula

The formula for gravitational potential energy is $U = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height.

Step2: Calculate potential energy on the moon

Given $m = 1200\ kg$, $g_{moon}=1.6\ m/s^{2}$, and $h = 350\ m$. Substitute into the formula: $U_{moon}=m\times g_{moon}\times h=1200\times1.6\times350 = 672000\ J$.

Step3: Know acceleration due to gravity on Earth

The acceleration due to gravity on Earth is $g_{earth}=9.8\ m/s^{2}\approx 10\ m/s^{2}$ (for simplicity in this comparison).

Step4: Calculate the ratio of potential energies

The ratio of the gravitational potential energy on Earth ($U_{earth}$) to that on the moon ($U_{moon}$) is $\frac{U_{earth}}{U_{moon}}=\frac{m\times g_{earth}\times h}{m\times g_{moon}\times h}=\frac{g_{earth}}{g_{moon}}$. Substituting $g_{earth} = 10\ m/s^{2}$ and $g_{moon}=1.6\ m/s^{2}$, we get $\frac{10}{1.6}=6.25$.