Question
Asked Sep 20, 2019
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A 5.00-kg block is moving at 6.00 m/s along a frictionless, horizontal surface toward a spring with force constant k=500 N/m that is attached to a wall (the figure (Figure 1)). The spring has negligible mass.

Find the maximum distance the spring will be compressed.
If the spring is to compress by no more than 0.550 m , what should be the maximum value of v0?
vo 6.00 m/s
k = 500 N/m
5.00
kg
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vo 6.00 m/s k = 500 N/m 5.00 kg

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Expert Answer

Step 1

Given:

Mass of the block = 5 kg

Velocity of the block = 6 m/s

Spring constant = 500 N/m

Step 2

Calculating the maximum compression in the spring:

Mass of the block = 5 kg
Initial velocity of the block, u = 6 m/s
1
Initial kinetic energy
:(m/s =90.J
(5 kg)(6m
miu
When the spring will be compressed to maximum
the velocity of the block will become zero
So, let the maximum compression in the spring:
X
Gain in spring energy
According to energy conservation,
Loss in kinetic energy = Gain in spring energy
1
So,
1
mu=90J
2
2
90J
180J
180J
0.36m2
500N m
x= 0.6m
help_outline

Image Transcriptionclose

Mass of the block = 5 kg Initial velocity of the block, u = 6 m/s 1 Initial kinetic energy :(m/s =90.J (5 kg)(6m miu When the spring will be compressed to maximum the velocity of the block will become zero So, let the maximum compression in the spring: X Gain in spring energy According to energy conservation, Loss in kinetic energy = Gain in spring energy 1 So, 1 mu=90J 2 2 90J 180J 180J 0.36m2 500N m x= 0.6m

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Step 3

Finding the required velo...

Compression in the spring, x 0.550 m
Spring constant, k= 500 N/m
(500m)(0.55m = 75.6J
Gain in spring energy
According to energy conservation
Loss in kinetic energy Gain in spring energy
If the initial velocity of the block is vo,
1
mv
Then loss in kinetic energy
So
30.24 (m
5 kg)
v=30.24 =5.5mls
help_outline

Image Transcriptionclose

Compression in the spring, x 0.550 m Spring constant, k= 500 N/m (500m)(0.55m = 75.6J Gain in spring energy According to energy conservation Loss in kinetic energy Gain in spring energy If the initial velocity of the block is vo, 1 mv Then loss in kinetic energy So 30.24 (m 5 kg) v=30.24 =5.5mls

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Tagged in

Science

Physics

Newtons Laws of Motion

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