Find a balls speed at a certain time with impulse chart

In summary, the ball's velocity at 4.0 s is 13 m/s, as it is moving in the positive direction at a constant velocity and there is no force acting on it during the time interval of interest.
  • #1
Ally385
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0

Homework Statement


A 0.155-kg ball, moving in the positive direction at 13 m/s, is acted on by the impulse shown in the graph below. What is the ball's speed at 4.0 s?

The graph is attached below.


Homework Equations



J = F Δt

The Attempt at a Solution



I thought that it might be zero because at 4 seconds the force is zero but now I look at it again and I'm thinking the equation might be 0 = 4-0 so the speed would be -4 but that doesn't make since.
 

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  • #2
Acceleration is proportional to force so acceleration is 0 when force is 0, not velocity. Any velocity increased by the acceleration when force is non-zero is retained when the force returns to 0. "F= ma", of course, so a= F/m and then velocity is the the integral of acceleration. In this problem, rather than finding the equations of those lines and integrating, because the integral can be interpreted as "area under the curve" the velocity is the area of that triangle.
 
  • #3
So that would be 2 right? It said that's the wrong answer. Should I not have multiplied the height as 2?
 
  • #4
Ally385 said:

Homework Statement


A 0.155-kg ball, moving in the positive direction at 13 m/s, is acted on by the impulse shown in the graph below. What is the ball's speed at 4.0 s?
[itex]\vec{J} = Δ\vec{p} = \vec{F}Δt[/itex]. It looks to me like the impulse is 2 kg m/s.

Thus, [itex]\vec{J} = \vec{p}_{final} - \vec{p}_{initial} = m(\vec{v}_{final} - \vec{v}_{initial})[/itex]. Solve for [itex]\vec{v}_{final}[/itex]

Hint: Because F = 0 over the interval [3, ∞), the acceleration is 0 in that interval as well. Thus, the velocity is the same at t = 3 as it is at t = 4.
 
  • #5


I would like to clarify that the equation J = F Δt is used to calculate the impulse, not the speed of an object. To find the speed of the ball at 4.0 seconds, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the ball's initial velocity is 13 m/s and the acceleration is 0 m/s^2 since there is no net force acting on the ball at 4.0 seconds. Therefore, the ball's speed at 4.0 seconds would still be 13 m/s.

It is important to note that the impulse graph does not directly provide information about the speed of the ball. It shows the change in momentum of the ball over time, and we can use this information to calculate the final velocity using the equation J = Δp = mΔv. In this case, the impulse is 0 Ns, which means there is no change in momentum and the final velocity remains the same as the initial velocity.

In order to find the speed at a certain time using the impulse graph, we would need to know the mass of the ball and the initial velocity, and then use the equation J = mΔv to calculate the change in velocity. We can then use this value to find the final velocity using the equation v = u + at.
 

5 Most Frequently Asked Questions about "Find a balls speed at a certain time with impulse chart"

1. How do I determine the speed of a ball at a specific time using an impulse chart?

To determine the speed of a ball at a specific time using an impulse chart, you will need to first plot the impulse data points on the chart. Then, using the impulse-momentum equation (p = m * v), you can calculate the momentum of the ball at the given time. Finally, use the equation v = p / m to calculate the speed of the ball at that time.

2. What is an impulse chart and how is it used to find a ball's speed at a certain time?

An impulse chart is a graphical representation of the force applied to an object over a specific period of time. It is used to find a ball's speed at a certain time by measuring the area under the curve of the chart, which represents the change in momentum of the ball.

3. Can I use any type of impulse chart to find a ball's speed at a certain time?

Yes, any type of impulse chart can be used to find a ball's speed at a certain time as long as it accurately represents the force applied to the ball over time.

4. What information do I need to have in order to find a ball's speed at a certain time using an impulse chart?

In order to find a ball's speed at a certain time using an impulse chart, you will need to know the mass of the ball, the force applied to the ball, and the time interval over which the force was applied.

5. Why is it important to know a ball's speed at a certain time?

Knowing a ball's speed at a certain time can provide valuable information for analyzing the motion and behavior of the ball. It can also help in predicting the trajectory and potential impact of the ball in a given situation.

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