Question

1. using what you know about the formulas for potential and kinetic energy, explain how mass and velocity (speed) affects kinetic energy. then, compare two scenarios: a 62 kg man running at 3.5 m/s a 55 kg woman running at 5 m/s which has more kinetic energy at the start, and why? (show your work for the math) 5. using what you know about the formulas for potential and kinetic energy, compare two scenarios: a spring with a spring constant of 112 n/m and pulled a distance of 0.42 m a rubberband with a spring constant of 123 n/m and pulled a distance of 0.12 m which has more potential energy and why? (show your work for the math)

Explanation:

Step1: Calculate kinetic energy for man

The formula for kinetic energy is \(K = \frac{1}{2}mv^{2}\). For the man, \(m = 62\space kg\) and \(v = 3.5\space m/s\).

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Step2: Calculate kinetic energy for woman

For the woman, \(m = 55\space kg\) and \(v = 5\space m/s\)

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Step3: Compare the two kinetic energies

Since \(687.5>379.75\), the woman has more kinetic energy.

Step4: Calculate potential energy for spring 1

The formula for elastic potential energy is \(U=\frac{1}{2}kx^{2}\). For spring 1, \(k = 112\space N/m\) and \(x = 0.42\space m\)

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Step5: Calculate potential energy for spring 2 (rubber - band)

For spring 2, \(k = 123\space N/m\) and \(x = 0.12\space m\)

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Step6: Compare the two potential energies

Since \(9.8784 > 0.8856\), the spring with \(k = 112\space N/m\) and \(x = 0.42\space m\) has more potential energy.

Answer:

The woman has more kinetic energy (\(K_{woman}=687.5\space J\) vs \(K_{man} = 379.75\space J\)). The spring with \(k = 112\space N/m\) and \(x = 0.42\space m\) has more potential energy (\(U_{1}=9.8784\space J\) vs \(U_{2}=0.8856\space J\))