A block of mass m 1 = 1.1 kg initially moving to the right with a speed of 4.9 m

Question

A block of mass m1 = 1.1 kg initially moving to the right with a speed of 4.9 m/s on a frictionless, horizontal track collides with a spring attached to a second block of mass m2 = 2.1 kg initially moving to the left with a speed of

1.4

m/s as shown in figure (a). The spring constant is 585N/m.

What if m1 is initially moving at 3.8 m/s while m2 is initially at rest?

(a) Find the maximum spring compression in this case.
x =  m

(b) What will be the individual velocities of the two masses (v1 and v2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete.)

Explanation / Answer

for maximum compression in the spring,

use TMEi = TMEf

K1 + U1 = K2 + U2

U1 = 0

so

0.5 m1 u1^2 = 0.5 me v2^2 + 0.5 kx^2

as V2 = 0

0.5 kx^2 = 0.5 m1 u1^2

x^2 = m1 u1^2/k

x^2 = 1.1* 4.9*4.9/(585)

x = 21.2 cm

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for velocities, from the conversation of momentums

we get

V1f = (m2-m1)V1/(m1+m2)

v1f = (2.1-1.1)* 4/(2.1+1.1)

v1f = 1.25 m/s

V2f = (V1f - v1i)

V2f = (1.25 - 4.9)

v2f = -3.65 m/s

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