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High School Physics : Calculating Kinetic Energy

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Example Question #31 : Energy

A 2kg book falls off the top of a 2.3m bookshelf. What is its velocity right before it hits the ground?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

$-6.71\frac{m}{s}$

$13.43\frac{m}{s}$

$3.36\frac{m}{s}$

$-26.86\frac{m}{s}$

$45.08\frac{m}{s}$

Correct answer:

$-6.71\frac{m}{s}$

Explanation:

The relationship between velocity and energy is:

$KE=\frac{1}{2}mv^2$

We know the mass, but we need to find the total kinetic energy.

Remember the law of conservation of energy: the total energy at the beginning equals the total energy at the end. In this case, we have only potential energy at the beginning and only kinetic energy at the end. (The initial velocity is zero, and the final height is zero).

PE_i=KE_f

If we can find the potential energy, we can find the kinetic energy. The formula for potential energy is PE=mgh .

Using our given values for the mass, height, and gravity, we can solve using multiplication. Note that the height becomes negative because the book is traveling in the downward direction.

$PE=2kg*-9.8\frac{m}{s^2}*-2.3m$

PE=45.08J

The kinetic energy will also equal 45.08J , due to conservation of energy.

Using this value and our given mass, we can calculate the velocity from our original kinetic energy equation.

$KE=\frac{1}{2}mv^2$

$45.08J=\frac{1}{2}*2kg*v^2$

45.08J=1kg*v^2

$45.08\frac{m^2}{s^2}=v^2$

$\sqrt{45.08\frac{m^2}{s^2}}=\sqrt{v^2}$

Since we are taking the square root, our answer can be either negative or positive. The final velocity of the book will be in the downward direction; thus, our final velocity should be negative.

$-6.71\frac{m}{s}=v$

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Example Question #11 : Calculating Kinetic Energy

Starting from rest a ball with a mass of 3kg experiences a constant force of 9N for 4s. Find the final kinetic energy (in joules) of the ball after 4s.

Possible Answers:

150J

320J

216J

200J

286J

Correct answer:

216J

Explanation:

Use Newton's laws to find the acceleration of the ball. Find the final speed of the ball, and then solve for kinetic energy.

Acceleration:

F=ma

$9N=(3kg)a\rightarrow a=\frac{9N}{3kg}=3\frac{m}{s^2}$

Final speed:

$V=V_{0}+at$

$V=0+\left(3\frac{m}{s^2}\right)4s=12\frac{m}{s}$

Kinetic energy:

$KE=\frac{1}{2}mv^2$

$KE=\frac{1}{2}(3kg)\left(12\frac{m}{s}^2\right)=216J$

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Example Question #31 : Energy And Work

Sam throws a 0.5kg rock off the edge of a 10m tall building at an angle of $35^{\circ}$ from the horizontal. The rock has an initial speed of $30\frac{m}{s}$ .

$\small g=-9.8\frac{m}{s^2}$

What is the final vertical kinetic energy right before the rock hits the ground?

Possible Answers:

123.1J

166J

98J

49J

88.4J

Correct answer:

123.1J

Explanation:

The formula for kinetic energy is $KE=\frac{1}2mv^2{}$ .

We first need to find the initial velocity in the vertical direction. To find the vertical velocity we use the equation $v_{i}* \sin(\Theta)=v_{iy}$ .

We can plug in the given values for the angle and initial velocity to solve.

$30\frac{m}{s}* \sin(35^{\circ})=v_{iy}$

$30\frac{m}{s}* (0.57)=v_{iy}$

$17.21\frac{m}{s}=v_{iy}$

We know that the rock is going to travel a net distance of -10m , as that is the distance between where the rock's initial and final positions. We now know the displacement, initial velocity, and acceleration, which will allow us to solve for the final velocity.

$v_f^2=v_1^2+2a\Delta y$

$v_f^2=(17.21\frac{m}{s})^2+2(-9.8\frac{m}{s^2})(-10m)$

$v_f^2=(296.18\frac{m^2}{s^2})+196\frac{m^2}{s^2}$

$v_f^2=492.18\frac{m^2}{s^2}$

$\sqrt{v_f^2}=\sqrt{492.18\frac{m^2}{s^2}}$

$v_{fy}=22.19\frac{m}{s}$

Now we have the mass and final velocity, allowing us to solve for the final kinetic energy.

$KE_f=\frac{1}{2}mv_f^2$

$KE_f=\frac{1}{2}(0.5kg)(22.19\frac{m}{s})^2$

KE_f=123.1J

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High School Physics : Calculating Kinetic Energy

Study concepts, example questions & explanations for High School Physics

All High School Physics Resources

Example Questions

Example Question #31 : Energy

Example Question #11 : Calculating Kinetic Energy

Example Question #31 : Energy And Work

All High School Physics Resources

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