Two lumps of clay having equal masses and speeds, but traveling in opposite directions, collide and stick together. Which of the following statements about this system of lumps must be true?

A. The momentum of the system is conserved during the collision.
B. The kinetic energy of the system is conserved during the collision.
C. The two masses lose all their kinetic energy during the collision.
D. The velocity of the center of mass of the system is the same after the collision as it was before the collision.

Hey there! Let me juggle some information for you and provide some answers with a touch of humor.

A. The momentum of the system is conserved during the collision. - True! Remember, momentum is like the clown's nose of physics – it ain't goin' anywhere unless acted upon by an external force. So, in this collision, the two lumps collide and stick together, but the total mass and speed remains the same, ensuring the momentum is conserved.

B. The kinetic energy of the system is conserved during the collision. - False! Sorry, but during this collision, the lumps stick together. It's like when a clown's shoe gets stuck in a puddle of custard, the kinetic energy goes for a toss, or more like a slip and slide. Some of that energy gets transferred to other forms like heat or sound.

C. The two masses lose all their kinetic energy during the collision. - False! While some kinetic energy may be lost during the collision, it's not "all" of it. Just like when an over-enthusiastic clown steps on a banana peel and loses some balance, but not all of it – there's still some energy left to keep the system rolling.

D. The velocity of the center of mass of the system is the same after the collision as it was before the collision. - True! The center of mass keeps its speed the same. It's like the clown car in a circus – even if the clowns bump into each other, the car keeps moving with the same velocity. So, the answer to this one is indeed true!

So, the correct statements are A - The momentum of the system is conserved during the collision, and D - The velocity of the center of mass of the system is the same after the collision as it was before the collision. Ta-da!

A. The momentum of the system is conserved during the collision.

When two objects collide and stick together, the total momentum of the system is conserved. This means that the sum of the momenta of the two objects before the collision is equal to the sum of their momenta after the collision.

So in this case, although the two lumps of clay initially have equal masses and speeds but are traveling in opposite directions, the total momentum before the collision is zero (since the momenta have opposite directions and cancel each other out). After the collision, the two lumps stick together and move as a single object with the same mass, which means the total momentum remains zero.

Hence, the correct statement is:

A. The momentum of the system is conserved during the collision.

To determine which statements about this system of lumps must be true, let's analyze each option:

A. The momentum of the system is conserved during the collision:
To check if the momentum is conserved in the collision, let's calculate the total momentum before and after the collision. The momentum of an object is given by the equation: momentum = mass × velocity.
Before the collision, the total momentum is the sum of the individual momenta of the two lumps. Since they have equal masses and speeds but are moving in opposite directions, their momenta have opposite signs. So, the total momentum before the collision is zero.
After the collision, the two lumps stick together and move as one object. The final momentum is the sum of their momenta, which will still be zero. Therefore, the momentum is conserved in this collision.

B. The kinetic energy of the system is conserved during the collision:
To determine if the kinetic energy is conserved, let's calculate the total kinetic energy before and after the collision. The kinetic energy of an object is given by the equation: kinetic energy = (1/2) × mass × (velocity)^2.
Before the collision, both lumps have equal masses and speeds, so their kinetic energy is the same. The total kinetic energy is the sum of their individual kinetic energies.
After the collision, the two lumps stick together, forming a larger object. As they stick together, the kinetic energy is converted into other forms, such as deformation energy or heat. Therefore, the kinetic energy is not conserved in this collision.

C. The two masses lose all their kinetic energy during the collision:
As mentioned in the previous explanation, the kinetic energy is not conserved in this collision. Some energy is lost as deformation energy or heat.

D. The velocity of the center of mass of the system is the same after the collision as it was before the collision:
The center of mass (COM) is the point where the total mass of an object or system can be considered to be concentrated. In this case, the lumps stick together and move as a single object after the collision. The velocity of the COM can be found by taking into account the masses and velocities of the two lumps.
Since the masses of the two lumps are equal and their speeds are equal but in opposite directions, the net momentum of the system is zero. The COM velocity can be calculated by dividing the total momentum by the total mass.
Before the collision, the net momentum was zero, so the velocity of the COM was also zero.
After the collision, the two lumps stick together and move as one object. The final velocity of the COM will still be zero, as the net momentum remains zero.
Therefore, the velocity of the center of mass of the system is the same after the collision as it was before the collision.

In conclusion, the statements that must be true about this system of lumps are:

A. The momentum of the system is conserved during the collision.
D. The velocity of the center of mass of the system is the same after the collision as it was before the collision.

A

B
D

Three choices are true. See if you can figure out which.