A box of mass M is dropped from a height h above a spring (spring constant k). A

Question

A box of mass M is dropped from a height h above a spring (spring constant k). An additional box of mass m is placed on top of the spring. Find the velocity of the first box just before it hits the second box on the spring. The two boxes have packing tape on their bottom and top, so that they stick together when they collide. Find the speed of the two boxes immediately after the collision. After the collision, the boxes will compress the spring some distance before coming to rest. Find that distance. Consider three periods of time (1) when the box is initially falling, (2) during the collision, and (3) while the spring is being compressed. For each of these time periods, explain whether momentum, energy, or both are conserved.

Explanation / Answer

a) the potential energy Mgh is convertd to kinetic energy.

so. Mgh= 0.5Mv2

=>v= root ( 2gh)

b) we will use consevation of momentum

let the final speed be v'

now,

Mv= (M+m)v'

=> v' = ( M/ M+ m ) v

=> v' = ( M/ M+ m ) root ( 2gh)

c) the kinetic energy of combined energy will be equal to spring potential energy

let the distance compressed be x,

so ,

0.5 * ( M+ m) *(v')2 = 0.5 kx2

=>x= root [(m+M)/k) ] * v'

=>x= root [(m+M)/k) ] * ( M/ M+ m ) root ( 2gh)

d) when the box is falling energy is conserved

during collision the the momentum is conserved and energy is conserved

during spring compression energy is conserved again

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.