Calculating Impulse from a Graph: How to Solve the Problem

In summary, the conversation discusses the concept of impulse and its relationship to force. It is suggested to break up the given graph into two triangles, one positive and one negative, and then calculate and add the impulse of both triangles. It is also mentioned that the integral of force equals the change in momentum and that an integral is the signed area between the x-axis and the curve.
  • #1
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Homework Statement


[The problem is in the attached image]


Homework Equations





The Attempt at a Solution


My best guess is to break up the graph into two triangles one positive, one negative and then calculate and add the impulse of both of these triangles... Is that what you're supposed to do?
 

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  • #2
Impulse is defined as the change in momentum, or Δp=Δ(mv)=mΔv. This quantity is related to the force F by the following logic.

F = dp/dt (you should memorize this equation; it's very useful.)

= d(mv)/dt
= m(dv)/dt
= m(dv/dt)
= ma, which is the definition of force.

Given this simple relationship,

∫dp = Δp = ∫F dt

What is an integral? An integral is the signed area between the x-axis (F=0) and the curve. So yes, calculate them separately, and then glue them together. Don't forget that everything below F=0 counts as negative impulse.
 
  • #3
Thank you :)
 

1. What is an "Impulse graphing question"?

An "Impulse graphing question" is a type of question that involves graphing the change in momentum over time for an object that experiences an impulse. It is commonly used in physics and engineering to analyze the effect of an external force on an object's motion.

2. How do you create an impulse graph?

To create an impulse graph, you first need to collect data on the object's initial and final momentum, as well as the time interval over which the impulse occurred. Then, plot the initial momentum on the y-axis and the time on the x-axis. Finally, draw a straight line from the point representing the initial momentum to the point representing the final momentum. The slope of this line will represent the impulse.

3. What is the relationship between impulse and change in momentum?

The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. This means that the greater the impulse, the greater the change in momentum. The direction of the impulse also affects the direction of the change in momentum.

4. How is an impulse calculated from an impulse graph?

The impulse can be calculated by finding the area under the impulse graph. This can be done by dividing the graph into geometric shapes (such as rectangles or triangles) and calculating the area of each shape. Then, add up all the areas to get the total impulse.

5. What are some real-life examples of impulse graphing?

Impulse graphing can be applied to a variety of real-life situations, such as a car crash, a collision between two moving objects, or a sports game where a ball is hit or kicked. It can also be used to analyze the efficacy of different safety measures, such as airbags in cars or helmets in sports. In engineering, impulse graphing can be used to design and test structures or machines that can withstand high forces or impacts.

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