Question

A car of mass 1000 kg moving with a speed 18 km/hr. on a horizontal surface,the coefficient of friction is 0.5 and the car colliding with a horizontal mounted spring.the spring constant is 6.25×10^3 Nm^-1.

then the calculate maximum compression of the spring.​

Answer 1

Answer:

Mass of the car M = 1000 kg

Speed of the car v = 18 km/h = 5 m/s

Spring constant k =6.25×10³N/m

Total kinetic energy of the car

$K=1/2mv²$

$⇒K=1/2×1000×5²$

$⇒K=125005 \: j$

After collision this kinetic energy will be converted into Potential Energy of the spring

If maximum compression of the spring is x then

$K=1/2kx²$

$⇒12500=1/2×6.25×10³×x²$

$⇒X²=12500×2/6250$

$⇒x²=2500/625$

$⇒x²=4$

$⇒x=√4$

$x=2m$

Therefore, the maximum compression in the spring is 2 m.

Answer 2

Answer:

Mass of the car M = 1000 kg

Speed of the car v = 18 km/h = 5 m/s

Spring constant k =6.25×10³N/m

Total kinetic energy of the car

K=1/2mv²K=1/2mv²

⇒K=1/2×1000×5²⇒K=1/2×1000×5²

⇒K=125005 \: j⇒K=125005j

After collision this kinetic energy will be converted into Potential Energy of the spring

If maximum compression of the spring is x then

K=1/2kx²K=1/2kx²

⇒12500=1/2×6.25×10³×x²⇒12500=1/2×6.25×10³×x²

⇒X²=12500×2/6250⇒X²=12500×2/6250

⇒x²=2500/625⇒x²=2500/625

⇒x²=4⇒x²=4

⇒x=√4⇒x=√4

x=2mx=2m

Therefore, the maximum compression in the spring is 2 m.