Question

1. an object with a moving kinetic energy of 2160j has a mass of 120kg. what is its velocity?
2. an object whose mass is 43kg is hanging on a thin wire. the object has a gravitational potential energy of 3160.5j. how high is the object above the ground?

Explanation:

Step1: Recall the formula for kinetic energy

The formula for kinetic energy \(K.E=\frac{1}{2}mv^{2}\), where \(K.E\) is kinetic energy, \(m\) is mass, and \(v\) is velocity. We are given \(K.E = 2160J\) and \(m=120kg\).

Step2: Rearrange the formula to solve for \(v\)

Starting from \(K.E=\frac{1}{2}mv^{2}\), we can solve for \(v\). First, multiply both sides by \(2\) to get \(2K.E=mv^{2}\). Then, divide both sides by \(m\): \(v^{2}=\frac{2K.E}{m}\). Substitute \(K.E = 2160J\) and \(m = 120kg\) into the formula: \(v^{2}=\frac{2\times2160}{120}\).

$$v^{2}=\frac{4320}{120}=36$$

Step3: Take the square root to find \(v\)

Since \(v^{2}=36\), then \(v=\sqrt{36}\).

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy \(P.E=mgh\), where \(P.E\) is gravitational potential energy, \(m\) is mass, \(g = 9.8m/s^{2}\) (acceleration due to gravity), and \(h\) is height. We are given \(P.E=3160.5J\), \(m = 43kg\), and \(g=9.8m/s^{2}\).

Step2: Rearrange the formula to solve for \(h\)

Starting from \(P.E=mgh\), we can solve for \(h\) by dividing both sides by \(mg\). So, \(h=\frac{P.E}{mg}\). Substitute \(P.E = 3160.5J\), \(m = 43kg\), and \(g=9.8m/s^{2}\) into the formula: \(h=\frac{3160.5}{43\times9.8}\).

$$h=\frac{3160.5}{421.4}=7.5m$$

Answer:

\(v = 6m/s\)