Question

A 2.5 kg block slides along a frictionless surface at 1.0 m/s . A second block, sliding at a faster 4.2 m/s , collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.8 m/s . What was the mass of the second block?

Answer 1

Using the principle of conservation of momentum, we can calculate the mass of the second block. The mass of the second block is approximately 1.078 kg.

Step-by-step explanation:

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

Let the mass of the second block be M.

Before the collision, the momentum of the first block is given by:

momentum1 = mass of first block * velocity of first block

momentum1 = 2.5 kg * 1.0 m/s = 2.5 kg∙m/s

After the collision, the momentum of the combined blocks is given by:

momentum final = (mass of first block + mass of second block) * velocity of combined blocks

momentum final = (2.5 kg + M) * 2.8 m/s

Since momentum is conserved, we can equate the two expressions:

2.5 * 1 = (2.5 + M) * 2.8

Simplifying the equation, we get:

M = (2.5 * 1) / 2.8 - 2.5

M = 1.078 kg

Therefore, the mass of the second block is approximately 1.078 kg.

Answer 2

To determine the mass of the second block in a momentum conservation problem, you calculate the sum of initial momenta and set it equal to the final momentum after collision. Solving for the unknown mass, you find that the mass of the second block is approximately 3.21 kg.

Step-by-step explanation:

To find the mass of the second block, you can use the principle of conservation of momentum, which states that in the absence of external forces, the total momentum of a system remains constant. The initial momentum of the system is the sum of the momenta of the two blocks before the collision, and the final momentum of the system is the momentum of the combined blocks after they stick together.

The formula for momentum is: p = m*v

Before the collision, block 1 has a momentum of 2.5 kg * 1.0 m/s = 2.5 kg*m/s, and block 2 has an unknown mass m and a momentum of m * 4.2 m/s. After the collision, the combined mass (2.5 kg + m kg) has a momentum of (2.5 kg + m) * 2.8 m/s.

By setting the total initial momentum equal to the total final momentum:

2.5 kg * 1.0 m/s + m * 4.2 m/s = (2.5 kg + m) * 2.8 m/s

Solving for m, the mass of the second block:

m = (2.5 kg * 2.8 m/s - 2.5 kg * 1.0 m/s) / (4.2 m/s - 2.8 m/s)

m = (7 kg*m/s - 2.5 kg*m/s) / 1.4 m/s

m = 4.5 kg*m/s / 1.4 m/s

m = 3.21 kg

Therefore, the mass of the second block is approximately 3.21 kg.