Question

Urgent!!!

Two students are testing out the law of conservation of momentum, by throwing balls of clay so that they collide. One student throws a 535g ball north at 12.4 m/s. The other throws a 725g ball south at 6.4 m/s. When the two balls of clay collide and form a single unit, what is the velocity of the combined unit?

1.86 m/s south

8.74 m/s north

1.86 m/s north

8.74 m/s south

Answer 1

The velocity of the combined unit after the collision is 1.58 m/s north.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision. The momentum of an object is given by the product of its mass and velocity.

In this case, the student throws a 535g ball north at 12.4 m/s, while the other student throws a 725g ball south at 6.4 m/s.

To find the velocity of the combined unit after the collision, we can calculate the total momentum before the collision by adding up the individual momenta of the two balls:

Momentum of ball 1 = mass of ball 1 * velocity of ball 1 = (0.535 kg)(12.4 m/s) = 6.634 kg·m/s north

Momentum of ball 2 = mass of ball 2 * velocity of ball 2 = (0.725 kg)(-6.4 m/s) = -4.64 kg·m/s south

The negative sign indicates that the velocity of ball 2 is in the opposite direction.

Now we can find the total momentum before the collision:

Total momentum before collision = momentum of ball 1 + momentum of ball 2 = 6.634 kg·m/s north + (-4.64 kg·m/s south) = 1.994 kg·m/s north

Since momentum is conserved, the total momentum after the collision will also be 1.994 kg·m/s north. Since the two balls stick together and form a single unit, their combined mass is the sum of their individual masses (0.535 kg + 0.725 kg = 1.26 kg).

Now we can find the velocity of the combined unit:

Velocity of combined unit = Total momentum after collision / Combined mass = 1.994 kg·m/s north / 1.26 kg = 1.58 m/s north

The velocity of the combined unit is 1.58 m/s north.

Answer 2

To solve this problem, we need to use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.

The momentum of an object is given by its mass multiplied by its velocity, so we can calculate the initial momentum of each ball before the collision:

- The northbound ball has a momentum of 535g * 12.4 m/s = 6644 g*m/s north

- The southbound ball has a momentum of 725g * (-6.4 m/s) = -4640 g*m/s north (note that the negative sign indicates southward direction)

Adding these momenta together, we get a total momentum of 6644 g*m/s - 4640 g*m/s = 2004 g*m/s north.

After the collision, the two clay balls stick together and move as a single unit. Let's call the mass of the combined unit "M" and its velocity "v". By conservation of momentum, we know that the total momentum of the combined unit after the collision must be the same as the total momentum before:

M * v = 2004 g*m/s north

To solve for v, we need to figure out the mass of the combined unit. This is simply the sum of the masses of the two original balls:

M = 535g + 725g = 1260g

Substituting this into the equation above, we get:

1260g * v = 2004 g*m/s north

Solving for v, we get:

v = 1.59 m/s north

Therefore, the combined unit moves 1.59 m/s north after the collision.

However, the answer choices given in the problem are in meters per second, not meters per second north/south. To convert the answer, we need to add a direction. Recall that the northbound ball had a positive velocity and the southbound ball had a negative velocity. Since the combined unit is moving northward, we know its velocity must be positive.

Therefore, the final answer is 1.59 m/s north, which corresponds to answer choice C.