Spring and mass problem, compression, avg force, displacemnt

In summary, the problem involves a 2kg box traveling at 5 m/s hitting a spring with a spring constant of 100 N/cm. The goal is to find the compression of the spring, the average force on the spring, and the distance the box rebounds from the spring. Taking into account friction, the compression of the spring can be found using the equation ½mv2 = ½kx2. The average force on the spring can be found using the force function F=-kx. If the surface has a coefficient of static friction of 0.15 and a coefficient of kinetic friction of 0.12, the distance the box rebounds can be found using the constant acceleration equations. However, if the surface is
  • #1
Steven2012
6
0

Homework Statement


A 2kg box traveling at a velocity of 5 m/s hits a spring (k=100 N/cm). Find
a. How much the spring will compress
b. What is the average force on the spring
c. If the surface has μs = 0.15 and μk = 0.12, how far will the box rebound from the spring
d. If the surface is smooth, how far will the box rebound from the spring

Homework Equations


½mv2 = ½kx2
F=ma
s=v0t+½at2

The Attempt at a Solution


a. ½mv2 = ½kx2
½*2*52 = ½*100*x2*100 (to change to m)
0.005 = x2 --> x=7.07cm

b. Favg = ½mv2
---this doesn't seem right---

c. F=ma
0.12*2*9.81*a --> 2.3a
---What is my F?--- Do I use Faverage ? ---
Then s=v0t+½at2

d. With no friction, v=5m/s
 
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  • #2
Steven2012 said:
b. Favg = ½mv2
---this doesn't seem right---
It isn't. What happened to friction?
 
  • #3
Steven2012 said:
a. ½mv2 = ½kx2
½*2*52 = ½*100*x2*100 (to change to m)
0.005 = x2 --> x=7.07cm

You need to take into account friction when calculating the compression of the spring

Steven2012 said:
b. Favg = ½mv2

.5kx^2 represents the total force exerted on the block over the interval x. How do you do find the average value of a function over an interval?
Also, make sure to once again take into account friction.
 
  • #4
A value for friction isn't introduced until "C". Therefore it is assumed as friction-less prior to this.
I know "A" is correct. It is easy enough. However, the solution I was given for "B" is Favg = (0+7.07+*100)/2 = 353.3N

This confuses me . I thought the equation should be Favg = ½mv2 But there isn't a sqr value.

What am i missing.

upload_2015-3-29_12-15-31.png
 
  • #5
For b) the force function is F=-kx. The integral of the function is (1/2)kx^2. They just used the force function instead of the work function to find the average force. Since the force function is linear the average force ends up being the fully compressed spring force divided by two.
c) The acceleration of the block is constant since the frictional force on it is constant, so you can use the constant acceleration equations to solve for the distance the block travels before stopping.
d) If there is no friction, then there is nothing to stop the block from just continuing to move at 5 m/s.
 
  • #6
Thx!
 

1. What is the spring and mass problem?

The spring and mass problem is a physics problem that involves a mass attached to a spring and its resulting motion when acted upon by a force, typically due to compression or extension of the spring.

2. What is compression?

Compression is the process of applying a force to a material or object that results in it being squeezed, shortened, or compacted. In the context of a spring and mass problem, compression occurs when the spring is compressed, resulting in a decrease in its length and an increase in force acting on the mass.

3. What is average force?

Average force is a measure of the overall force applied to an object over a period of time. In the context of a spring and mass problem, it can be calculated by dividing the total force applied to the mass by the time it takes for the spring to return to its original position.

4. What is displacement?

Displacement is a measure of the change in an object's position from its initial position. In the context of a spring and mass problem, displacement refers to the change in the position of the mass from its initial position due to the compression or extension of the spring.

5. How do you calculate displacement in a spring and mass problem?

To calculate displacement in a spring and mass problem, you can use the equation x = F/k, where x is the displacement, F is the force applied to the mass, and k is the spring constant. This equation assumes that the spring is ideal and follows Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement.

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