Water Barrels
A car in the shown diagram collides into the water barrels typically found on highways. The barrels act as a spring to reduce impact and deflect 2 meters. If the car weighs 100 kg, and the barrels have a spring constant of 25 kN/m, what is the velocity (m/s) of the car right before impact with the wall?
Expand Hint
The spring’s potential energy:
$$$U=\frac{kx^{2}}{2}$$$
where
$$k$$
is the spring constant, and
$$x$$
is the compressed distance.
Hint 2
The car’s kinetic energy:
$$$KE=\frac{1}{2}mv^2$$$
where
$$m$$
is the mass, and
$$v$$
is the velocity.
The spring's potential energy:
$$$U=\frac{kx^{2}}{2}=\frac{25kN\cdot (2m)^2}{m\cdot 2}=50kN\cdot m=50,000\:N\cdot m$$$
where
$$k$$
is the spring constant, and
$$x$$
is the compressed distance. The car's kinetic energy:
$$$KE=\frac{1}{2}mv^2=\frac{1}{2}(100kg)v^2=50kg\cdot v^2$$$
where
$$m$$
is the mass, and
$$v$$
is the velocity. Because energy is conserved,
$$U=KE$$
:
$$$50kg\cdot v^2=50,000N\cdot m$$$
$$$v=31.62\:m/s$$$
31.62 m/s
Time Analysis
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