Question

To test the resiliency of its bumper during low-speed collisions, a 2 840-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 6.00 106 N/m and compresses 3.98 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall

Answer 1

Answer:

V= 1.82 m/s

Explanation:

Given that

mass , m = 2840 kg

Spring constant ,K = 6 x 10⁶ N/m

Compression in the spring , x = 3.98 cm

Lets take speed of the car before impact = V

Now by using energy conservation

$\dfrac{1}{2}Kx^2=\dfrac{1}{2}mV^2$

$Kx^2=mv^2$

$V=\sqrt{\dfrac{Kx^2}{m}}$

Now by putting the values in the above equation

$V=\sqrt{\dfrac{6\times 10^6\times (3.98\times 10^{-2})^2}{2840}}$

V= 1.82 m/s

Therefore the speed of the car before impact will be 1.82 m/s.