Hooke's Law and Force in a Slingshot

[mcnealymt]

Homework Statement

A 46g rock is placed in a slingshot and the rubber band is stretched. The force of the rubber band on the rock is shown by the graph in the figure(Figure 1) .

http://session.masteringphysics.com/problemAsset/1073689/4/10.P37.jpg


a)Is the rubber band stretched to the right or to the left?
b)Does this rubber band obey Hooke's law?
c)What is the rubber band’s spring constant k?
d)The rubber band is stretched 29cm and then released. What is the speed of the rock?

Homework Equations

Fsp= -kΔx

The Attempt at a Solution

a) Left because the displacement is negative and therefore the Fsp must be positive?
b) Yes, it obeys Hooke's Law because as the displacement increases, the amount of force does?
c) Isn't it just the slope of the given graph?
d) Honestly not sure where to begin.

 

[Sunil Simha]

a)Is the rubber band stretched to the right or to the left?
b)Does this rubber band obey Hooke's law?
c)What is the rubber band’s spring constant k?
d)The rubber band is stretched 29cm and then released. What is the speed of the rock?

The Attempt at a Solution

a) Left because the displacement is negative and therefore the Fsp must be positive?
b) Yes, it obeys Hooke's Law because as the displacement increases, the amount of force does?
c) Isn't it just the slope of the given graph?
d) Honestly not sure where to begin.

a) and b) are correct but b) can be amended as " the force is proportional to the displacement and in opposition to it and hence obeys the law".

For c) yes it is the slope.

For d) are you aware of the expression for energy stored in the band as a function of the stretch(x)? If yes, try conservation of energy. If no, try deriving the expression using
Energy stored=∫F.dx for the band and then use conservation of energy.

 

[mcnealymt]

Alright, thank you. It turns out I forgot to convert the mass to kg.

This is what I got:

Spring Potential Energy= Kinetic Energy
Us (initial)=KE (Final)
.5kx^2= .5mv^2

V= Square root of ( K*X/m)

k= spring constant
X= change in displacement
m= mass of the rock

 

[Sunil Simha]

V= Square root of ( K*X/m)

You mean square root of Square root of ( K*(X^2)/m) right? That was unintentional on your part I guess.

Anyway, Enjoy Physics.

 

[mcnealymt]

Lol, fail on my part... thanks Sunil Simha.