Question

By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships

Answer 1

Answer:

Explanation:

Given that,

Stiffness K=460N/m

Extension e=0.37m

Two balls attached to a string

First ball has mass and velocity

M1 =8kg and V1~ =4i +11j +0k

For the second ball

M2 =4kg and V2~ =-3i+10j +0k

a. Momentum of system?

Momentum is given as

P = m1•V1~ +m2•V2~

P= 8(4i +11j +0k) +4(-3i+10j +0k)

P=32i + 88j + 0k -12i +40j + 0k

P= 20i + 128j + 0k kgm/s

2. Magnitude of each velocity is given as

V1²=Vx² +Vy² + Vz²

V1² =4²+11²+0²

V1² =137

V1 =√137

V1=11.705m/s

Also V2

V2²= Vx² +Vy² +Vz²

V2²=(-3)²+(10)² +0²

V2²=109

V2 = √109

V2 =10.44m/s

Ktot= k(trans) +k(rel)

d. K(trans) =½m1•V1²

K(trans) =½×8×11.705²

K(trans) = 548.03J

e. K(rel) =½m2•V2²

K(rel) =½ ×4×10.44²

K(rel) = 217.99J

c. Then, K(tot)=K(trans)+k(rel)

K(tot) =548.03+217.99

K(tot) = 766.02J