Which of the following is true when an object of mass m moving on a horizonta...

Question:

Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="M&gt;m" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 16.8px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">M>mM>m, which is initially at rest on the surface?

a) The collision is elastic.

b) All of the initial kinetic energy of the less-massive object is lost.

c) The momentum of the objects that are stuck together has a smaller magnitude than the initial momentum of the less massive object.

d) The speed of the objects that are stuck together will be less than the initial speed of the less-massive object.

e) The direction of motion of the objects that are stuck together depends on whether the hit is a head on collision.

Linear Momentum

Linear momentum is a mathematical representation of motion in vector form in which the mass and velocity of a body are related in its basic form in classical mechanics. Its mathematical representation is presented in the following way,

<span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="p=mv" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 16.8px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">p=mvp=mv

Here,

<span id="MathJax-Element-3-Frame" class="mjx-full-width mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="m=Massv=Velocity" role="presentation" style="box-sizing: border-box; line-height: 0; text-align: center; font-size: 16.8px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 5.473em; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; width: 10000em; position: relative; display: table-cell !important;">m=Massv=Velocitym=Massv=Velocity

Answer and Explanation:

PART A) False. If the mass sticks to the biggest object, the collision is inelastic.

PART B) False. In inelastic collisions, there is a partial loss of the kinematic energy of the object but it does not mean a total loss, the larger mass can keep moving.

PART C) False. For conservation of linear momentum, the momentum of both bodies must be conserved and be the same.

PART D) True. This is true because the larger mass would require more energy to move than the smaller mass.

PART E) False. The direction only depends on the orientation with respect to a coordinate axis that has the collision in its initial moment and that triggers a trajectory in its final phase.