Question

Consider an object consisting of two balls connected by a spring, whose stiffness is460 N/m. The object has been thrown through the air and is rotating and vibrating as it moves. At a particular instant the spring is stretched 0.37 m, and the two balls at the ends of the spring have the following masses and velocities:

⢠1: 8 kg, ⹠4, 11, 0 ⺠m/s


⢠2: 4 kg, â¹ â3, 10, 0 ⺠m/s


(a) For this system, calculate

p with arrowsys = ? kg · m/s

(b) Calculate v with arrowCM ? = m/s


(c) Calculate Ktot ?= J


(d) Calculate Ktrans ? = J


(e) Calculate Krel ? = J

Answer 1

V = 1.6777 m/s , 10.667 , 0 m/s

P = ( 20, 128, 0 ) kg-m/s

`K_(tot)` = 766 J

`K_(trans)` = 699.3 J

Krel = 66.7 J

Step-by-step explanation:

given data

Stiffness K = 460 N/m

Extension e = 0.37 m

solution

we know that here that center of mass is express as

V =
`(m1* v1 + m2* v2)/(m1+m2)` ................1

V1 =
`(8* 4 + 4* -3)/(8+4)`

V1 = 1.6777 m/s

V2 =
`(8* 11 + 4* 10)/(8+4)`

V2 = 10.667 m/s

V3 =
`(8* 0 + 4* 0)/(8+4)`

V3 = 0 m/s

and

P system is

P =
`M_(tot) * V_(cm)`

P = (8+4) × ( 1.6777 , 10.667 , 0 )

P = ( 20, 128, 0 ) kg-m/s

and

`K_(tot)` = K1 + K2

`K_(tot)` = 0.5 × m × v1² + 0.5 × m × v2²

`K_(tot)` = 0.5 × 8 ×
`√(4^2+11^2+0^2)` + 0.5 × 4 ×
`√(-3^2+10^2+0^2)`

`K_(tot)` = 766 J

and

`K_(trans)` = 0.5 ×
`M_(tot)` × ( V(cm)²)

`K_(trans)` = 0.5 × (8+4) ×
`(√(1.667^2+12.667^2))^2`

`K_(trans)` = 699.3 J

and

Krel =
`K_(tot)` -
`K_(tot)`

Krel = 766 J - 699.3 J

Krel = 66.7 J