Relating position and force to speed

In summary, the conversation centered around finding the speed of a 1.8-kg box on a frictionless surface, given a force-position graph. The discussion included topics such as the work-energy theorem, calculating work done, and the relationship between force, distance, and work. The correct method for finding the speed was determined to be using the area under the force-position curve, which led to the correct answer of 1 m/s.
  • #1
Capncanada
53
0

Homework Statement



The force graphed in figure is applied to a 1.8-{\rm kg} box initially at rest at x = 0 on a frictionless, horizontal surface.
(Graph is attached)

Homework Equations



F=ma (?)

The Attempt at a Solution



Don't know how to relate speed to these two scalars..
 

Attachments

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  • #2
You haven't stated what the problem is. At all.
 
  • #3
I need to find the speed when position = 5, 10 and 15cm. Sorry.
 
  • #4
What level of math goes with your course?
 
  • #5
It's physics 2A, I'm not having trouble with math I'm having trouble with finding the units of m/s out of units like force and position.
 
  • #6
Well, if it's calculus based, we might give one answer.

Trig. & algebra another.

Elementary algebra. ?

How is work done related to kinetic energy.
 
  • #7
I had to take calculus to get into this course.
 
  • #8
A simple application of the work-energy theorem should get you on your way.
 
  • #9
What does area under the graph represent?
 
  • #10
So F=ma can give me the acceleration of the object, I have no units of time to convert to speed here
 
  • #11
The area represents work done?
 
  • #12
think about force time distance. Look at cepheid's suggestion.
 
  • #13
Capncanada said:
The area represents work done?

Yes.
 
  • #14
I can solve for work done here but that leaves me with units of (kg*m^2)/s^2, I do not know how to get to speed here. This is probably very obvious, but I'm not seeing it.
 
  • #15
cepheid said:
A simple application of the work-energy theorem should get you on your way.
Cap'ncanada,

What's this theorem?
 
  • #16
F=ma?
 
  • #17
Capncanada said:
F=ma?
That's force.

Look at the units again. remember, you're looking for speed.
 
  • #18
Err, W=KE=1/2mv^2?

Im having a lot of trouble with physics...
 
  • #19
Capncanada said:
F=ma?

No, that is not the work-energy theorem. That is Newton's 2nd Law. The work-energy theorem relates the work done on an object to its change in energy. If you haven't encountered it before (which seems strange) you can always look it up.

By the way, the work, of course, has dimensions of force*distance, therefore its units are Newton-metres = joules.
 
  • #20
Capncanada said:
Err, W=KE=1/2mv^2?

Im having a lot of trouble with physics...

That's pretty much it, but it should be that the work done on the object is equal to its CHANGE in kinetic energy. Therefore W = ΔKE = (1/2)mvf2 - (1/2)mvi2, where vf and vi are the final and initial velocities respectively.
 
  • #21
but v_i will equal zero here yes?

I tried solving for when d= 5cm and it comes out and v_f comes out to 1m/s which is incorrect.
 
  • #22
Capncanada said:
but v_i will equal zero here yes?

I tried solving for when d= 5cm and it comes out and v_f comes out to 1m/s which is incorrect.

Okay. Well you understand all of the physics now, so it must just be an issue with arithmetic.
Can you post your solution for the x = 5 cm case? We can try and see where you went wrong.

Yes, vi = 0 in this problem. Sorry if it seemed like I was being pedantic before. I was just making sure to get across the correct statement of the work-energy theorem.
 
  • #23
No I appreciate the thoroughness of your explanations, I've been struggling all semester with this stuff and I need to understand it to a better extent, payed tutoring might be in my future. :(

Anyways,

W=F*d
W=18N*.05m
W=0.9J

W=KE=(1/2)mv^2
v^2=2KE/m
v^2=2(0.9J)/1.8kg
v=1m/s
 
  • #24
Capncanada said:
No I appreciate the thoroughness of your explanations, I've been struggling all semester with this stuff and I need to understand it to a better extent, payed tutoring might be in my future. :(

Anyways,

W=F*d
W=18N*.05m
W=0.9J

W=KE=(1/2)mv^2
v^2=2KE/m
v^2=2(0.9J)/1.8kg
v=1m/s

Well, it looks to me like the area underneath the curve is a triangle with a base of 5 cm and a height of ~18 N. Is the area of that triangular region just equal to base*height? Hint: what shape of region actually has an area of 18 N * 5 cm? What portion of that region is made up by the triangle?
 
  • #25
Ahh... So I was supposed to divide the work I found in half since A=1/2b*h. Getting right answers now.
 
  • #26
Capncanada said:
Ahh... So I was supposed to divide the work I found in half since A=1/2b*h. Getting right answers now.

Yeah exactly. Your mistake was that W = F*Δx is NOT true if the force is not constant. In this case the force is a function of position F = F(x). The more general formula for work is W = ∫F(x)dx. That's why work is equal to the area under the force-position curve. In this case, since F(x) was linear, that curve was a triangle, and we could just evaluate the area geometrically (no need to integrate).

You can see that the more general formula reduces to the simpler one when the force is not varying. If F(x) = F = constant, then W = ∫F(x)dx = F∫dx = FΔx. You can see that, in that simpler case, the force-position curve would be flat, and the area underneath would be a rectangle (and simply multiplying base*height would work).

So, the summary is that the more general integration or "area under the curve" method always works, whereas the simpler "force*distance" method only works if the curve is flat (constant force).
 

What is the relationship between position and force?

The relationship between position and force is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be, and the greater the object's mass, the slower its acceleration will be.

How does force affect speed?

Force directly affects an object's speed by causing it to accelerate. According to Newton's second law of motion, the greater the force applied to an object, the greater its acceleration will be. This means that the more force a person exerts on an object, the faster the object will move. However, other factors such as friction and air resistance can also affect an object's speed.

Does an object's position affect its speed?

An object's position does not directly affect its speed, but it can indirectly affect it through factors such as gravity and air resistance. For example, an object that is higher above the ground will experience less air resistance and may have a greater speed than an object at a lower position. Additionally, an object's position can affect the amount of force required to move it, which can also impact its speed.

How can we calculate an object's speed based on its position and force?

To calculate an object's speed based on its position and force, we can use the formula speed = distance/time, where distance is the object's change in position and time is the duration of the change. We can also use Newton's second law of motion, which states that acceleration is equal to the net force divided by the object's mass. By knowing the object's mass and the net force acting on it, we can calculate its acceleration and then use the formula speed = acceleration * time to determine its speed.

How can we use the relationship between position and force to our advantage?

Understanding the relationship between position and force can be beneficial in various fields such as engineering, sports, and transportation. For example, engineers can use this relationship to design more efficient machines and structures, athletes can use it to optimize their performance, and transportation companies can use it to improve the speed and fuel efficiency of vehicles. By understanding this relationship, we can also make better predictions and calculations for various scenarios involving objects in motion.

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