Suppose two blocks of ice are heading toward each other. block A has a mass of 4.24 kg and is traveling at 2.24 m/s. Block B has a mass 4.42 kg and is traveling at 2.24 in the opposite direction. After the collision they are traveling in the same speed. what is the speed they are traveling?
To calculate the final speed of the two blocks after collision, 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 is given by the product of its mass and velocity. So, we can calculate the momentum of block A before the collision as:
Momentum of A before collision = mass of A × velocity of A
= 4.24 kg × 2.24 m/s
Similarly, the momentum of block B before the collision is:
Momentum of B before collision = mass of B × velocity of B
= 4.42 kg × (-2.24 m/s) (as it is in the opposite direction)
The total momentum before the collision can be calculated by adding the individual momenta:
Total momentum before collision = Momentum of A before collision + Momentum of B before collision
Now that we have the total momentum before the collision, we can calculate the total momentum after the collision. Since the two blocks stick together and move in the same speed:
Total momentum after collision = (mass of A + mass of B) × final velocity
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
Using this equation, we can solve for the final velocity. Rearranging the equation, we get:
final velocity = (momentum of A before collision + momentum of B before collision) / (mass of A + mass of B)
Substituting the given values, the calculation is as follows:
momentum of A before collision = 4.24 kg × 2.24 m/s = 9.4976 kg·m/s
momentum of B before collision = 4.42 kg × (-2.24 m/s) = -9.8848 kg·m/s
mass of A + mass of B = 4.24 kg + 4.42 kg = 8.66 kg
final velocity = (9.4976 kg·m/s - 9.8848 kg·m/s) / 8.66 kg
final velocity ≈ -0.0447 m/s
Thus, the two blocks will be traveling at a speed of approximately -0.0447 m/s after the collision. Note that the negative sign indicates that the blocks will be moving in the opposite direction.