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webassign.net Question Total Points Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer Assignment Scoring Your last submission is used for your score 1 B PIRE 001. My A Two-Body Collision with a Spring A block of mass m-2.3 kg initially moving to the right with a speed of 4.8mn m/s on a frictionless, horizontal track collides with a spring attached to a second block of mass m2 = 3.5 kg initially moving to the left with a speed of 27 m/s as shown in figure (a). The spring constant is 580 N/m. Amovng es with moving-eth a spring attached: (a) before the (A) Find the velocities of the two blocks after the collision (B) During the collision, at the instant block 1 is moving to the right with a velocity of 0.8 m/s as in figure (b), determine the velocity of block 2 (C) Determine the distance the spring is compressed at that instant.

Explanation / Answer

m1 = 2.3 kg

v1i = 4.8 m/s

m2 = 3.5 kg

v2i = - 2.7 m/s

v1f = ?

v2f = ?

using conservation of momentum

m1 v1i + m2 v2i = m1 v1f + m2 v2f

(2.3) (4.8) + (3.5) (- 2.7) = 2.3 v1f + 3.5 v2f

2.3 v1f + 3.5 v2f = 1.6

v1f = (1.6 - 3.5 v2f)/2.3 eq-1

using conservation of kinetic energy

m1 v21i + m2 v22i = m1 v21f + m2 v22f

(2.3) (4.8)2 + (3.5) (- 2.7)2 = 2.3 v21f + 3.5 v22f

2.3 v21f + 3.5 v22f = 78.5

using eq-1

2.3 ((1.6 - 3.5 v2f)/2.3)2 + 3.5 v22f = 78.5

v2f = 3.25 m/s

using eq-1

v1f = (1.6 - 3.5 v2f)/2.3 =  (1.6 - 3.5 (3.25)/2.3 = - 4.25 m/s

b)

m1 = 2.3 kg

v1i = 4.8 m/s

m2 = 3.5 kg

v2i = - 2.7 m/s

v1f = 0.8 m/s

v2f = ?

using conservation of momentum

m1 v1i + m2 v2i = m1 v1f + m2 v2f

(2.3) (4.8) + (3.5) (- 2.7) = 2.3 (0.8) + 3.5 v2f

v2f = - 0.0714 m/s

using conservation of energy

m1 v21i + m2 v22i = m1 v21f + m2 v22f + k x2

(2.3) (4.8)2 + (3.5) (- 2.7)2 = 2.3 (0.8)2 + 3.5 (- 0.0714)2 + (580) x2

x = 0.36 m

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