SOLUTION (A) Find the velocity v 2 f when block 1 has velocity +3.00 m/s. Write
ID: 1339953 • Letter: S
Question
SOLUTION
(A) Find the velocity v2f when block 1 has velocity +3.00 m/s.
Write the conservation of momentum equation for the system and solve forv2f.
(1)
m1v1i + m2v2i = m1v1f + m2v2f
(B) Find the compression of the spring.
Use energy conservation for the system, noticing that potential energy is stored in the spring when it is compressed a distance x.
Ei = Ef
Substitute the given values and the result of part (a) into the preceding expression, solving for x.
x = 0.173 m
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REMARKS The initial velocity component of block 2 is ?2.50 m/s because the block is moving to the left. The negative value for v2f means that block 2 is still moving to the left at the instant under consideration.
QUESTION Is it possible for both blocks to come to rest while the spring is being compressed? Explain. Hint: Look at the momentum in Equation (1). (Select all that apply.)
No, it is not possible.Yes, if the two blocks initially have initial momenta with equal magnitudes and opposite directions.Yes, if the two blocks initially have equal masses.Yes, if the ratio of the two initial speeds of the blocks equals the inverse ratio of their masses.Yes, if the two blocks initially have initial velocities with equal magnitudes and opposite directions.
Consider from Equation (1) what total momentum the system must have at the instant when the two blocks would be at rest. Use the equation to find how the masses, velocities, and momenta must be related for that to happen.
PRACTICE IT
Use the worked example above to help you solve this problem. A block of mass m1 = 1.50 kg, initially moving to the right with a velocity of +3.63 m/s on a frictionless horizontal track, collides with a massless spring attached to a second block of mass m2 = 2.11 kg moving to the left with a velocity of
?2.17 m/s,
(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.
The response you submitted has the wrong sign. 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 = m/s
(b) Find the compression of the spring.
x = m
Explanation / Answer
a)
m1 * v1i + m2 * v2i = m1 * v1f + m2 * v2f
v2f = m1 * v1i + m2 * v2i - m1 * v1f / m2
v2f = 1.6 * 4 + 2.1 * -2.5 - 1.6 * 3 / 2.1
v2f = -1.74 m/s
b)
Ei = Ef
0.5 * m1 * v1^2 + 0.5 m2 * v2^2 + 0 = 0.5 * m1 * v1f^2 + 0.5 * m2 * v2f^2 + 0.5 * k * x^2
then by putting all the values we calculate x
x = 0.173 m
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