An object of known mass M with speed v0 travels toward a wall. The object collides with it and bounces away from the wall in the opposite direction in which the object was initially traveling. The wall exerts an average force F0 on the object during the collision. A student must use the equation Δp⃗ =F⃗ Δt to determine the change in momentum of the object from immediately before the collision to immediately after the collision. Which side of the equation could the student use to determine the change of the object's momentum?

Δp⃗ , because the mass of the object and the initial speed of the object are known.

A

F⃗ Δt, because the average force exerted on the object during the collision is known.

B

Either side of the equation may be used because the mass of the object, the initial speed of the object, and the average force exerted on the object during the collision are known.

C

Neither side of the equation may be used because there are too many unknown quantities before, during, and after the collision.

The impulse theorem states that the change in momentum of an object is equal to the impulse, which is the product between the average force applied and the duration of the collision:

[tex]\Delta p = F \Delta t[/tex]

where

[tex]\Delta p[/tex] is the change in momentum

F is the average force

[tex]\Delta t[/tex] is the duration of the collision

In this problem, neither side of the equation can be used to measure the change in momentum. In fact:

- The change in momentum (left side) is given by

[tex]\Delta p = m(v-u)[/tex]

where

m is the mass of the object

u is the initial velocity

v is the final velocity

Here the final velocity is not known, so it's not possible to use this side of the equation

- The impulse (right side) is given by

[tex]F\Delta t[/tex]

here the average force is known, however the duration of the collision is not known, so it's not possible to use this side of the equation.

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snehashish65 snehashish65 · Answer 2 · 2021-10-16T18:52:52+02:00

Neither side of the equation may be used because there are too many unknown quantities before, during, and after the collision. Therefore, option (C) is correct.

According to the impulse-momentum theorem, "The change in momentum of an object is equal to the impulse produced by the object. Where the impulse is expressed as the product of average force on the object and the duration of collision (reaction time)".

The expression is given as,

..............................................(1)

Here, [tex]\delta p[/tex] is the change in momentum, [tex]F_{av.}[/tex] is the average force and t is the reaction time.

In equation (1), [tex]\delta p[/tex] is the change in momentum which is given as,

[tex]\delta p = m(v-u)[/tex]

Here, m is the mass, v and u are the final and initial velocities of object respectively.

Since, object's mass (m) and velocities are not given. Therefore, left hand side of equation (1) cannot be used to determine the change of object's momentum.

Also, right hand side of equation (1) requires the duration of collision (t), which is missing in the problem.

Thus, we can conclude that there are various unknown variables present in the problem, for which neither side of the equation may be used to determine change in momentum of object. Hence, option (C) is correct.

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