A block of mass 1.0 kg is attached to a horizontal spring that has a force constant of 2,000 N/m as shown in figure (a). The spring is compressed 3.0 cm and is then released from rest as in figure (b).
A block of mass 1.0 kg is attached to a horizontal spring that has a force constant of 2,000 N/m as shown in figure (a). The spring is compressed 3.0 cm and is then released from rest as in figure (b).
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Question
Transcribed Image Text:A Block-Spring System
A block of mass 1.0 kg is attached to
horizontal spring that has a force constant of 2,000 N/m as shown in figure (a). The spring is compressed 3.0 cm and
then released from rest as in figure (b).
(a) A block attached to a spring is pushed inward
from an initial position x -0 by an external
agent. (b) At position x, the block is released
from rest and the spring pushes it to the right.
x = 0
(For the following, when entering a mathematical expression, do not substitute numerical values; use variables only.)
(a) Calculate the speed of the block as it passes through the equilibrium positio
x = 0 if the surface is frictionle
SOLUTION
Conceptualize This situation has been discussed before, and it is easy to visualize the block being pushed to the right by the spring and moving with some speed at x = 0.
Categorize We identify the system as the block and model the block as [--Select--
Vsystem.
Analyze In this situation, the block starts with v, = 0 at x, = -3.0 cm, and we want to find v, at x = 0.
Use the following equation to find the work done by the spring with x
"max
= x;:
2.
w=z*max
Work is done on the block, and its speed changes. The conservation of energy equation reduces to the work-kinetic energy theorem. Use that theorem to find the speed at x = 0 (Use the following as necessary: k, xmay and m):
2
W =
+Ew = V
m s
V = V
Substitute numerical values to calculate the speed (in m/s):
m/s
Finalize Although this problem could have been solved in a previous chapter, it is presented here to provide contrast with the following part (b), which requires the techniques of this chapter.
Transcribed Image Text:(b) Calculate the speed of the block as it passes through the equilibrium position if a constant friction force of 8.0 N retards its motion from the moment it is released.
SOLUTION
Conceptualize The correct answer must be -Select---
|that found in part (a) because the friction force retards the motion.
Categorize We identify the system as the block and the surface,
---Select---
system because of the work done by the spring. There is a nonconservative force acting within the system: the friction between the block and the surface.
(Use the following as necessary: d, f, k, x
*max and m.
Analyze Write the equation shown:
w, = AK + AEint = (Gmv - c
0) +
Solve for v
w - fd)
Substitute for the work done by the spring:
V; = V
Substitute numerical values to calculate the speed (in m/s):
m/s
Finalize As expected, this value is -Select---
2 the speed found in part (a).
EXERCISE
The block from the Example is placed on a different rough surface, and its speed at x = 0 is 0.55 m/s. What is the frictional force (in N) in this case? (Enter the magnitude.)
Hint
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