1.9 kg block slides along a frictionless surface at 1.8 m/s. A second block, sliding at a faster 4.5 m/s, collides with the first from behind and sticks to it. The final velocity of the combined blocks is 3.5 m/s.

What was the mass of the second block?

How do you set this equation up? I tried a couple of different ways and nothing worked, I only have one attempt left before I get the question wrong. Please help

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object can be calculated as the product of its mass and velocity (momentum = mass * velocity).

Let's assume the mass of the first block is m1 and the mass of the second block is m2. Given that the velocity of the first block is 1.8 m/s, the velocity of the second block is 4.5 m/s, and the final velocity of the combined blocks is 3.5 m/s, we can set up the equation as follows:

(m1 * 1.8) + (m2 * 4.5) = (m1 + m2) * 3.5

Now, we can solve for the mass of the second block (m2):

1.8m1 + 4.5m2 = 3.5m1 + 3.5m2

Rearranging the terms, we get:

1.8m1 - 3.5m1 = 3.5m2 - 4.5m2

-1.7m1 = -1m2

Dividing both sides by -1, we get:

1.7m1 = 1m2

Therefore, the mass of the second block is equal to 1.7 times the mass of the first block.

To solve this problem, we can apply the principles of conservation of momentum. The total momentum before the collision should be equal to the total momentum after the collision, assuming no external forces are at play.

Let's break down the problem step by step:

Step 1: Write down what is given in the problem:
- Mass of the first block (m1) = 1.9 kg
- Initial velocity of the first block (v1) = 1.8 m/s
- Initial velocity of the second block (v2) = 4.5 m/s
- Final velocity of the combined blocks (vf) = 3.5 m/s

Step 2: Define the variables:
- Mass of the second block (m2) = unknown (let's solve for it)

Step 3: Apply the principle of conservation of momentum:
The total momentum before the collision (initial momentum) is the sum of the momenta of each block separately:
Initial total momentum = (m1 * v1) + (m2 * v2)

The total momentum after the collision is the sum of the momenta of the combined blocks:
Final total momentum = (m1 + m2) * vf

Step 4: Equate the initial total momentum to the final total momentum:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf

Step 5: Substitute the given values into the equation:
(1.9 kg * 1.8 m/s) + (m2 * 4.5 m/s) = (1.9 kg + m2) * 3.5 m/s

Step 6: Simplify and solve for m2:
3.42 kg m/s + 4.5 m/s * m2 = 6.65 kg m/s + 3.5 m/s * m2
0.5 m/s * m2 = 3.23 kg m/s
m2 = 3.23 kg m/s / 0.5 m/s
m2 = 6.46 kg

Therefore, the mass of the second block is approximately 6.46 kg.

It's important to note that when setting up the equation, we consider the conservation of momentum, which states that the total momentum before the collision must be equal to the total momentum after the collision. By solving the equation, we can determine the unknown mass of the second block.

3.23

Use conservation of linear momentum.

M1*V1 + M2*V2 = (M1+M2)*V3

The only unknown is M2 in this case, so you can solve for it.

1.9*1.8 + M2*4.5 = (1.9 + M2)*3.5
3.42 + M2 = 6.65
M2 = ____ kg