Question

calculate the change in the kinetic energy (ke) of the bottle when the mass is increased. use the formula ( ke=\frac{1}{2}mv^{2} ), where ( m ) is the mass and ( v ) is the speed (velocity). assume that the speed of the soda bottle falling from a height of 0.8 m will be 4 m/s, and use this speed for each calculation. record your calculations in table a of your student guide. when the mass of the bottle is 0.125 kg, the ke is ( square ) ( kgcdot m^{2}/s^{2} ). when the mass of the bottle is 0.250 kg, the ke is ( square ) ( kgcdot m^{2}/s^{2} ). when the mass of the bottle is 0.375 kg, the ke is ( square ) ( kgcdot m^{2}/s^{2} ). when the mass of the bottle is 0.500 kg, the ke is ( square ) ( kgcdot m^{2}/s^{2} ).

Explanation:

Step1: Calculate KE for \(m = 0.125\space kg\)

Use the formula \(KE=\frac{1}{2}mv^{2}\), with \(v = 4\space m/s\) and \(m=0.125\space kg\).
\(KE=\frac{1}{2}\times0.125\times(4)^{2}=\frac{1}{2}\times0.125\times16 = 1\)

Step2: Calculate KE for \(m = 0.250\space kg\)

Use the formula \(KE=\frac{1}{2}mv^{2}\), with \(v = 4\space m/s\) and \(m = 0.250\space kg\).
\(KE=\frac{1}{2}\times0.250\times(4)^{2}=\frac{1}{2}\times0.250\times16=2\)

Step3: Calculate KE for \(m = 0.375\space kg\)

Use the formula \(KE=\frac{1}{2}mv^{2}\), with \(v = 4\space m/s\) and \(m = 0.375\space kg\).
\(KE=\frac{1}{2}\times0.375\times(4)^{2}=\frac{1}{2}\times0.375\times16 = 3\)

Step4: Calculate KE for \(m = 0.500\space kg\)

Use the formula \(KE=\frac{1}{2}mv^{2}\), with \(v = 4\space m/s\) and \(m = 0.500\space kg\).
\(KE=\frac{1}{2}\times0.500\times(4)^{2}=\frac{1}{2}\times0.500\times16=4\)

Answer:

When the mass of the bottle is \(0.125\space kg\), the \(KE\) is \(1\space kg\cdot m^{2}/s^{2}\).
When the mass of the bottle is \(0.250\space kg\), the \(KE\) is \(2\space kg\cdot m^{2}/s^{2}\).
When the mass of the bottle is \(0.375\space kg\), the \(KE\) is \(3\space kg\cdot m^{2}/s^{2}\).
When the mass of the bottle is \(0.500\space kg\), the \(KE\) is \(4\space kg\cdot m^{2}/s^{2}\).