Formula 1 Energy

#599 / Dynamics Medium

In the shown figure, a 30 kN F1 car races around a track at 200 kilometers per hour. What is its kinetic energy in MJ?

Expand Hint

$$$Force=mass\times acceleration$$$

Hint 2

Kinetic Energy:

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

where $$m$$ is the mass and $$v$$ is the velocity.

In the problem statement, the weight of the F1 car is given as a force. To find the mass:

$$$F=m\times a$$$

where $$F$$ is the force, $$m$$ is the mass, and $$a$$ is the acceleration due to gravity. Thus,

$$$30kN=m\times 9.81\frac{m}{s^2}$$$

$$$m=\frac{30,000kg\cdot (m/s^2)}{9.81m/s^2}=3,058.1\:kg$$$

Next, convert the velocity into meters per second:

$$$200 \frac{km}{hr}\cdot \frac{1,000m}{km}\cdot \frac{hr}{60min}\cdot \frac{min}{60s}=55.56\:m/s$$$

Finally, to solve for Kinetic Energy:

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

where $$m$$ is the mass and $$v$$ is the velocity.

$$$KE=\frac{1}{2}(3,058.1kg)(55.56m/s)^2=4,719,295\:kg\cdot \frac{m^2}{s^2}$$$

$$$=4,719,295N\cdot m=4.7\:MJ$$$

4.7 MJ

Time Analysis

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