Apackage of mass m is released from rest at a warehouse loading dock and slides down a 3.0-m-high frictionless chute to a waiting truck. unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute.

a. what is the speed of the package of mass m right before the collision?

b. suppose the packages stick together. what is their common speed after the collision? is the total mechanical energy for the system including both packages conserved in this case? if not, what is the difference of the mechanical energies before and after the collision?

c. suppose the collision between the packages is perfectly elastic. to what height does the package of mass m rebound? is the total linear momentum for the system including both packages conserved before and after this perfectly elastic collision? why or why not?

The speed of the package of mass m right before the collision

Their common speed after the collision

Height achieved by the package of mass m when it rebounds

Explanation:

Have a look to the diagrams attached below.

a.To find the speed of the package of mass m right before collision we have to use law of conservation of energy.

where is Kinetic energy and is Potential energy.

and

Considering the fact   we will plug out he values of the given terms.

So

Keypoints:

KE = Kinetic Energy and PE = Potential Energy

b.Now when the package stick together there momentum is conserved.

Using law of conservation of momentum.

where .

Plugging the values we have

Cancelling m from both sides and dividing 3 on both sides.

Law of conservation of energy will be followed over here.

c.Now the collision is perfectly elastic

We have to find the value of for m mass.

As here we can use that if both are moving in right ward with then there is a   velocity when they have to move leftward.

The best option is to use the formulas given in third slide to calculate final velocity of object .

So

Now using law of conservation of energy.

The linear momentum is conserved before and after this perfectly elastic collision.

So for part a we have the speed for part b we have their common speed and for part c we have the rebound height .

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explanation: