Q11DQ - University Physics with Modern Physics

Question

A falling brick has a mass of 1.5 kg and is moving straight downward with a speed of 5.0 m/s. A 1.5-kg physics book is sliding across the floor with a speed of 5.0 m/s. A 1.5-kg melon is traveling with a horizontal velocity component 3.0 m/s to the right and a vertical component 4.0 m/s upward. Do all of these objects have the same velocity? Do all of them have the same kinetic energy? For both questions, give your reasoning. 

Step-by-Step Solution

Answer

The velocities are not same, and the kinetic energy will be same.

Step 1: Describe the Kinetic Energy

The expression for the Kinetic Energy is given by,

$\mathit{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

Here, m  is the mass of an object, and v  is the velocity of the object.

Step 2: Determine whether all of the objects have the same velocity and kinetic energy

The brick is moving in a downward direction. The velocity of the brick is .

$\left({\overrightarrow{v}}_b\right)=-5.0 \mathrm{m}/\mathrm{s}$

 The velocity of the physics book is $\left({\overrightarrow{v}}_b\right)=-5.0 \mathrm{m}/\mathrm{s}$.

 

The velocity of the melon is $\left({\overrightarrow{v}}_m\right)=3.0\hat{i}+4.0\hat{j}$. Here, $\hat{i}$ , and $\hat{j}$ are unit vectors along the horizontal and vertical direction respectively.

 

The magnitude of the velocity is,

$$\begin{gathered} \left|{\overrightarrow{v}}_m\right|=\sqrt{{\left(3\right)}^2+{\left(4\right)}^2} \\ =\sqrt{25} \\ =5 \mathrm{m}/\mathrm{s} \end{gathered}$$

 

Therefore, the velocities are not the same.

 

Calculate the kinetic energy of the brick.

$$\begin{gathered} K_b=\frac{1}{2}m{v}_b^2 \\ =\frac{1}{2}\left(1.5 \mathrm{kg}\right){\left(-5 \mathrm{m}/\mathrm{s}\right)}^2 \\ =18.75 \mathrm{J} \end{gathered}$$

 

Calculate the kinetic energy of the physics book.

$$\begin{gathered} K_p=\frac{1}{2}m{v}_p^2 \\ =\frac{1}{2}\left(1.5 \mathrm{kg}\right){\left(5 \mathrm{m}/\mathrm{s}\right)}^2 \\ =18.75 \mathrm{J} \end{gathered}$$

 

Calculate the kinetic energy of the melon.

$$\begin{gathered} K_m=\frac{1}{2}m{v}_m^2 \\ =\frac{1}{2}\left(1.5 \mathrm{kg}\right){\left(5 \mathrm{m}/\mathrm{s}\right)}^2 \\ =18.75 \mathrm{J} \end{gathered}$$

 

Therefore, the kinetic energy of all bodies are the same.