Collision and Impulse question

• SmokeyBear
In summary, when a male bighorn sheep collides head-first with another male, the peak acceleration is 34 m/s2 and the duration of the collision is 0.27 s. With a mass of 90.0 kg, the magnitude of the impulse is 413 Ns and the average force is 4,587.6 N. The area between the plot and the axis in Figure 9-11 is used to calculate the impulse, but the average acceleration should be used to calculate the speed.
SmokeyBear
When a male bighorn sheep runs head-first into another male, the rate at which its speed drops to zero is dramatic. Figure 9-11 gives a typical graph of the acceleration a versus time t for such a collision, with the acceleration taken as negative to correspond to an initially positive velocity. The peak acceleration has magnitude 34 m/s2 and the duration of the collision is 0.27 s. Assume that the sheep's mass is 90.0 kg. What are the magnitudes of the impulse and average force due to the collision?

I know impulse is equal to the change in momentum (J = mΔv). So first I found vo by using v = vo + at. After plugging in the numbers, I got vo = -9.18 m/s. I then plugged this into the formula J = mΔv = m(v - vo), where v = 0 m/s, to get 826.2 Ns as the impulse. Unfortunately, the book has exactly half of that as the answer (413 Ns) as the answer. The way they did it was finding the area between the plot and the axis of Figure 9-11, then multiplying it by 90 kg. I understand why this works, but what I don't understand is how my answer comes out to be twice as large.

Any help is greatly appreciated. Thanks.

SmokeyBear said:
I understand why this works, but what I don't understand is how my answer comes out to be twice as large.
The acceleration is not constant. Use the average acceleration in your formula for speed.

How did I miss that? Thanks a lot!

1. What is collision and impulse?

Collision is a physical event in which two or more objects come into contact with each other and exchange energy. Impulse refers to the change in momentum that occurs during a collision.

2. How is impulse calculated?

Impulse is calculated as the product of the force applied and the time during which it is applied. It is represented by the equation J = F * Δt, where J is the impulse, F is the force, and Δt is the time interval.

3. What are the types of collisions?

There are two types of collisions: elastic and inelastic. In an elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision, only momentum is conserved.

4. How does the mass and velocity of objects affect collision and impulse?

Objects with larger masses will have a greater momentum and require more force to change their velocity compared to objects with smaller masses. Similarly, objects with higher velocities will have a greater impulse compared to objects with lower velocities during a collision.

5. Can you explain the concept of conservation of momentum in collisions?

The law of conservation of momentum states that the total momentum in a closed system remains constant before and after a collision. This means that the total momentum of the objects involved in a collision will be the same before and after the collision, regardless of any external forces acting on the system.

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