A 1.2 kg box slides down a frictionless ramp from a height of 3.00 m. At the bot
ID: 1409351 • Letter: A
Question
A 1.2 kg box slides down a frictionless ramp from a height of 3.00 m. At the bottom of the ramp this box collides elastically with a 1.8 kg box initially at rest. The second box then slides across a horizontal frictionless floor and hits a spring (k = 400 N/m). a) What is the speed of the 1.2 kg block at the bottom of the ramp? b) What is the speed of the 1.8 kg block after the collision? c) What is the maximum compression of the spring? 15. A 40 g bullet is fired vertically at into 150 g baseball initially at rest. The bullet lodges in the baseball and, after the collision, the baseball/bullet rises to a height of 200 m. What was the firing speed of the bullet?Explanation / Answer
I think you are asking the answer of (14) and (15). So I am solving these two questions.
(14) (a) Potential energy lost by 1.2 kg block = mgh
And this is equal to gain in kinetic energy of the block = 0.5mv^2
So, mgh = 0.5mv^2
=> v^2 = 2gh = 2*9.81*3 = 58.86
v = 7.67 m/s
(b) Let the velocity of 1.2 kg block be v1 and that of 1.8 kg block be v2 after the collision.
applying conservation of momentum -
1.2*7.67 = 1.2v1 + 1.8v2
=> 1.2v1 + 1.8v2 = 7.2
=> v1 = 6 - 1.5v2 ----------------------(I)
Now since the collision is perfectly elastic, so energy will be constant.
So, 0.5*1.2*7.67^2 = 0.5*1.2*v1^2 + 0.5*1.8*v2^2
=> 1.2v1^2 + 1.8v2^2 = 70.6
putting the value of v1 from (I)
=> 1.2*(6 - 1.5v2)^2 + 1.8V2^2 = 70.6
=> 1.2(36 - 18v2 + 2.25v2^2) + 1.8v2^2 = 70.6
=> 4.5v2^2 - 21.6v2 + 43.2 = 70.6
=> v2^2 - 4.8v2 - 6.09 = 0
=> (v2 - 2.4)^2 = 11.85
=> v2 - 2.4 = 3.44
=> v2 = 5.84 m/s discarding the negative sign.
(c) Let the maximum compression in the spring be x.
So, 0.5*1.8*5.84^2 = 0.5*400*x^2
=> x^2 = 0.1534752
=> x = 0.39 m.
(15) let the firing speed of the bullet be v.
applying conservation of energy - loss in kinetic energy = gain in potential energy
0.5*0.04*v^2 = (0.04+0.15)*9.81*200 = 372.78
=> v^2 = 18639
=> v = 136.52 m/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.