Respuesta :
1) The variable that is different in the two cases is [tex]\Delta t[/tex], the duration of the collision
2) The change in momentum is the same in the two cases
3) The impulse is the same in the two cases
4) Case B will experience a greater force
Explanation:
1)
The variable that is different in the two cases is [tex]\Delta t[/tex], the duration of the collision.
In fact, in the first case the wall is padded: this means that the collision will be "softer" and therefore will last longer, so the duration of the collision, [tex]\Delta t[/tex], will be larger.
In the second case instead, the wall is unpadded: this means that the collision is "harder" and so it will last less time, therefore the duration of the collision [tex]\Delta t[/tex] will be smaller.
2)
The change in momentum in the two cases is the same.
In fact, the change in momentum is given by:
[tex]\Delta p = m(v-u)[/tex]
where:
m is the mass of the student
u is the initial velocity
v is the final velocity
In both cases, we have:
m = 75 kg
u = 8 m/s
v = 0 (they both comes to rest)
Therefore, the change in momentum is
[tex]\Delta p = (75)(0-8)=-600 kg m/s[/tex]
3)
The impulse in the two cases is the same.
In fact, impulse is defined as the product of force applied, F, and duration of the collision, [tex]\Delta t[/tex]:
[tex]J=F \Delta t[/tex]
However, the force can be rewritten as product of mass (m) and acceleration (a), according to Newton's second law:
[tex]F=ma[/tex]
So the impulse is
[tex]J=ma\Delta t[/tex]
The acceleration can be rewritten as rate of change of velocity:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
So the impulse becomes
[tex]J=m\frac{\Delta v}{\Delta t}\Delta t = m\Delta v[/tex]
So, the impulse is equal to the change in momentum: and since in the two cases the change in momentum is the same, the impulse is the same as well.
4)
The force in the collision is related to the impulse by
[tex]J=F\Delta t[/tex]
where
J is the impulse
F is the force
[tex]\Delta t[/tex] is the duration of the collision
The equation can be rewritten as
[tex]F=\frac{J}{\Delta t}[/tex]
In the two situations described in the problem (A and B), we already said that the impulse is the same (because the change in momentum is the same). However, in case A (padded wall) the time [tex]\Delta t[/tex] is longer, while in case B (unpadded wall) the time [tex]\Delta t[/tex] is shorter: since the force F is inversely proportional to the duration of the collision, this means that in case B the student will experience a greatest force compared to case A.
Learn more about impulse:
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The variable in the two cases has been time of collision.
The change in momentum in both the cases has been equal.
The impulse in both the cases has been the same.
The greatest force has been applied in case B.
The collision has been described as the contact of one body with another. There has been force of both the body that has been exerted with the collision.
Collision of Student with wall
The collision with padded wall has been softer, and is resulted with the longer duration of the collision. The collision with an unpadded wall has been hard and will be for a short duration of time.
The variable in the two cases has been time of collision.
- The change in momentum has been described as the product of mass and velocity. In both the collisions, there has been same mass and velocity of the student.
Thus, the change in momentum in both the cases has been equal.
- The impulse has been defined as the force that has been responsible for the collision. The impulse has been equivalent to the change in momentum.
The change in momentum in with the cases has been the same. Thus, the impulse in both the cases has been the same.
- The force has been described as the impulse applied per unit time.
The time of collision has been inversely proportional to force. Since, the time of collision has been longer for padded wall in Case A as compared to case B, the force has been smaller for case A.
Thus, the greatest force has been applied in case B.
Learn more about collision, here:
https://brainly.com/question/13876829
