(a) Determine the velocity of block 2 at the instant when block 1 is moving to t

Question

(a) Determine the velocity of block 2 at the instant when block 1 is moving to the right with a velocity of +3.00 m/s, as shown in Figure b. (Indicate the direction with the sign of your answer.)
  m/s

(b) Find the compression of the spring.
.173  
Your response differs from the correct answer by more than 10%. Double check your calculations. m

EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK!

Use the values from PRACTICE IT to help you work this exercise. Consider the instant that block 2 is at rest.

(a) Find the velocity of block 1. (Indicate the direction with the sign of your answer.)
v1f =   
What is the total momentum before the collision? Write an expression for the total momentum after the collision and solve for the velocity of block 1. m/s

(b) Find the compression of the spring.
x =   
Mechanical energy is conserved. Any kinetic energy that is missing from the system has been converted into potential energy in the spring. m

Explanation / Answer

m1 = 1.5 Kg
m2 = 2.11 Kg
v1i = 3.63 m/s
v2i = - 2.17 m/s

(a)
Using Momentum Conservation,
m1*v1i + m2*v2i = m1*v1f + m2*v2f
1.5 * 3.63 - 2.11*2.17 = 1.5*3 + 2.11*v2f
Solving for v2f ,
v2f = - 1.72 m/s
Velocity of block 2 = - 1.72 m/s

(b)
Spring constant, k = 6.08*10^2 N/m
Initial Kinetic Energy = 0.5*m1*v1i^2 + 0.5m2*v2i ^2
Initial Kinetic Energy = 0.5*1.5 * 3.63^2 +0.5* 2.11*2.17^2
Initial Kinetic Energy = 14.85 J

Final Kinetic Energy = 0.5*m1*v1f^2 + 0.5m2*v2f ^2
Final Kinetic Energy = 0.5*1.5 * 3.0^2 +0.5* 2.11*1.72^2
Final Kinetic Energy = 9.87 J

Spring Energy = Kinetic Energy Initial - Kinetic Energy Final

0.5*k*x^2 = 14.85 - 9.87
x = sqrt((4.98*2)/(6.08*10^2))
x = 0.128 m
Compression, x = 12.8 cm

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