Work Energy And Power Question 225
Question: A 2 kg block slides on a horizontal floor with a speed of4m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compresses by Critical Thinking
Options:
A) 8.5 cm
B) 5.5 cm
C) 2.5 cm
D) 11.0 cm
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let the blow compress the spring by x before stopping.
Kinetic energy of the block = (P.E of compressed spring) + work done against function. $ \frac{1}{2}\times 2\times {{( 4 )}^{2}}=\frac{1}{2}\times 10,000\times x^{2}+( +15 )\times x $
$ 10,000x^{2}+30x-32=0 $
$ \Rightarrow 5,000x^{2}+15x-16=0 $
$ \therefore x=-\frac{15\pm \sqrt{{{( 15 )}^{2}} \pm - 4\times (5000)(-16)}}{2\times 5000} $
$ =0.055m=5.5cm. $
