Question

1. what is the motional kinetic energy of a 150 - gram (* convert to kg) object moving at a velocity of 100m/s?
2. an object has a moving kinetic energy of 96j. its velocity is 4m/s. what is its mass?
3. an object with a motional kinetic energy of 1125j has a mass of 250kg. what is its velocity?

Explanation:

Step1: Convert mass to kg

Given mass \(m = 150g\). Since \(1kg=1000g\), then \(m=\frac{150}{1000}kg = 0.15kg\). Velocity \(v = 100m/s\). The formula for kinetic energy is \(K.E=\frac{1}{2}mv^{2}\).

Step2: Calculate kinetic energy

Substitute \(m = 0.15kg\) and \(v = 100m/s\) into the formula \(K.E=\frac{1}{2}\times0.15\times(100)^{2}\). First, calculate \((100)^{2}=10000\). Then \(\frac{1}{2}\times0.15\times10000= 750J\).

Step3: For problem 8

Given \(K.E = 96J\) and \(v = 4m/s\). From \(K.E=\frac{1}{2}mv^{2}\), we can solve for \(m\). Rearranging the formula gives \(m=\frac{2K.E}{v^{2}}\). Substitute \(K.E = 96J\) and \(v = 4m/s\) into the formula: \(m=\frac{2\times96}{4^{2}}\). Calculate \(4^{2}=16\) and \(2\times96 = 192\). Then \(m=\frac{192}{16}=12kg\).

Step4: For problem 9

Given \(K.E = 1125J\) and \(m = 250kg\). From \(K.E=\frac{1}{2}mv^{2}\), we solve for \(v\). Rearranging gives \(v=\sqrt{\frac{2K.E}{m}}\). Substitute \(K.E = 1125J\) and \(m = 250kg\) into the formula: \(v=\sqrt{\frac{2\times1125}{250}}\). Calculate \(2\times1125 = 2250\), then \(\frac{2250}{250}=9\). So \(v=\sqrt{9}=3m/s\).

Answer:

1. The kinetic energy is \(750J\).
2. The mass is \(12kg\).
3. The velocity is \(3m/s\).