Q2E - University Physics with Modern Physics

Question

The maximum height a typical human can jump from a crouched start is about 60 cm . By how much does the gravitational potential energy increase for a 72 kg person in such a jump? Where does this energy come from?

Step-by-Step Solution

Answer

The increase in the gravitational potential energy in such a jump is.

The energy comes from the kinetic energy.

Step 1: Identification of the given data

The given data can be listed below as:

• The mass of the person is, m = 72 kg.
• The maximum height a human can jump is, $h_2=60\hspace{0.33em}cm\times \frac{{10}^{-2}\hspace{0.33em}m}{1\hspace{0.33em}cm}=60\times {10}^{-2} m$.

Step 2: Significance of the potential energy

The potential energy is described as the energy that an object possesses while at rest. Moreover, the potential energy is also described as the stored energy of an object.

Step 3: Determination of the increase in the gravitational potential energy

The equation of the gravitational potential energy is expressed as:

 

$U=mg(h_2-h_1)$ 

 

Here, U is the gravitational potential energy, m is the mass of the mountain climber, g is the acceleration due to gravity, $h_2$ is the maximum height a human can jump and $h_1$ is the standing position of the human.

 

Substitute the values in the above equation.

 

$$\begin{gathered} \mathrm{U}=\left(72 \mathrm{kg}\right)\left(9.8 \mathrm{m}/{\mathrm{s}}^2\right)\left(0.60 \mathrm{m}-0 \mathrm{m}\right) \\ =\left(705.6 \mathrm{kg}\times \mathrm{m}/{\mathrm{s}}^2\right)\left(0.6 \mathrm{m}\right) \\ =423 \mathrm{kg}\times {\mathrm{m}}^2/{\mathrm{s}}^2\times \frac{1\mathrm{J}}{1\mathrm{kg}\times {\mathrm{m}}^2/{\mathrm{s}}^2} \\ =423 J \end{gathered}$$ 

 

Thus, the increase in the gravitational potential energy in such a jump is 423 J.

Step 4: Determination of the energy

Here, the energy is coming from the kinetic energy which the person provides himself while starting the jump. The kinetic energy comes because of the potential elastic energy from the muscles of that person.

 

Thus, the energy comes from the kinetic energy.