A 5.5 kg object with a speed of 4.0 m/s collides head-on with a 13 kg object moving toward it with a speed of 3.0 m/s. The 13 kg object stops dead after the collision.

(a) What is the final speed of the 5.5 kg object?
m/s
(b) Is the collision elastic?
Yes
No

To solve this problem, we can apply the principles of conservation of momentum and kinetic energy. Let's break down the steps to find the final speed of the 5.5 kg object and determine if the collision is elastic.

Step 1: Determine the initial momentum of each object.
The initial momentum (P) of an object can be calculated by multiplying its mass (m) by its velocity (v). Using the given information, we can calculate the initial momentum of each object:

For the 5.5 kg object:
Initial momentum = mass × velocity = 5.5 kg × 4.0 m/s = 22.0 kg·m/s (since velocity is a vector, we use the magnitude)

For the 13 kg object:
Initial momentum = mass × velocity = 13 kg × (-3.0 m/s) = -39 kg·m/s (since the object is moving in the opposite direction, we take the negative value)

Step 2: Determine the final momentum of each object.
Since we know that the 13 kg object stops dead after the collision, its final momentum is zero. The final momentum of the 5.5 kg object is unknown and will be calculated.

For the 13 kg object:
Final momentum = 0

For the 5.5 kg object:
Final momentum = mass × final velocity

Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. Therefore, we can write the equation:

Initial momentum of 5.5 kg object + Initial momentum of 13 kg object = Final momentum of 5.5 kg object + Final momentum of 13 kg object

Using the given information, we can substitute the values into the equation:

22.0 kg·m/s + (-39 kg·m/s) = 5.5 kg × final velocity + 0

Step 4: Solve for the final velocity of the 5.5 kg object.
Simplifying the equation:

Final velocity = (22.0 kg·m/s + (-39 kg·m/s)) / 5.5 kg
Final velocity = -4.0 m/s

Therefore, the final velocity of the 5.5 kg object is -4.0 m/s.

Step 5: Determine if the collision is elastic.
An elastic collision is one in which both momentum and kinetic energy are conserved. To determine if the collision is elastic, we need to check if the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

The initial kinetic energy of the system can be calculated as:
KE_initial = 0.5 × mass_1 × (velocity_1)^2 + 0.5 × mass_2 × (velocity_2)^2

For the 5.5 kg object:
KE_initial = 0.5 × 5.5 kg × (4.0 m/s)^2 = 44 J

For the 13 kg object:
KE_initial = 0.5 × 13 kg × (-3.0 m/s)^2 = 58.5 J

The final kinetic energy of the system can be calculated by comparing it to the final momentum:

For the 5.5 kg object:
KE_final = 0.5 × 5.5 kg × (final velocity)^2 = 0.5 × 5.5 kg × (-4.0 m/s)^2 = 44 J

Since the initial kinetic energy and final kinetic energy are equal, we can conclude that the collision is elastic.

To summarize the answers:
(a) The final speed of the 5.5 kg object is -4.0 m/s.
(b) The collision is elastic.