A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is [2024]
1 m
6 m
5 m
2 m
(4)
sin30°=h10⇒h=5
At maximum compression
using Work-Energy Theorem,
Wgravity+Wfriction+Wspring=ΔKE
mgh-μmg(2+x)-12kx2=0-0
5×10×5-12×5×10(2+x)-12100×x2=0
250-50x2-[50+25x]=0
200-50x2-25x=0
2x2+x-8=0
x=-1±12+4×2×82×2⇒x=-1±654≈1.77m
Nearest answer is 2m.
