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A package of mass m is released from rest at a warehouse
Chapter 10, Problem 43P(choose chapter or problem)
A package of mas \(m\) is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of Figure P10.43 to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass \(2m\) from the bottom of the chute.
a. Suppose the packages stick together. What is their common speed after the collision?
b. Suppose the collision between the packages is perfectly elastic. To what height does the package of mass \(m\) rebound?
Equation Transcription:
Text Transcription:
m
2m
m
Questions & Answers
QUESTION:
A package of mas \(m\) is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of Figure P10.43 to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass \(2m\) from the bottom of the chute.
a. Suppose the packages stick together. What is their common speed after the collision?
b. Suppose the collision between the packages is perfectly elastic. To what height does the package of mass \(m\) rebound?
Equation Transcription:
Text Transcription:
m
2m
m
ANSWER:Step 1 of 2
Part a
We are required to calculate the common speed of the packages after they collide.
Let the initial speed of the package of mass is
. It covers a height of 3.0 m until it collides the package of mass
.
Using the energy conservation of the mass ,
Now, given m
So, m/s
m/s
Therefore, the speed of the package of mass is 7.67 m/s.
After the collision, the packages stick together. Let the common speed of the packages now be .
Thus, from momentum conservation,
m/s
m/s
Therefore, the required common speed is 2.56 m/s.