Two blocks of mass 0.1 kg and 0.2 kg approach each other on a frictionless
surface at velocities of 0.4 and 1 m/s respectively. If the blocks collide and remain
together, calculate their joint velocity after the collision.
To calculate the joint velocity of the blocks after the collision, we can use the principle of conservation of momentum.
The momentum before the collision is given by the sum of the individual momenta of the two blocks:
Momentum before collision = (mass of block 1 * velocity of block 1) + (mass of block 2 * velocity of block 2)
= (0.1 kg * 0.4 m/s) + (0.2 kg * 1 m/s)
= 0.04 kg⋅m/s + 0.2 kg⋅m/s
= 0.24 kg⋅m/s
Since the blocks collide and remain together, the total mass after the collision is the sum of the individual masses:
Total mass after collision = mass of block 1 + mass of block 2
= 0.1 kg + 0.2 kg
= 0.3 kg
Using the principle of conservation of momentum, the joint velocity after the collision can be calculated by dividing the momentum before the collision by the total mass after the collision:
Joint velocity after collision = Momentum before collision / Total mass after collision
= 0.24 kg⋅m/s / 0.3 kg
= 0.8 m/s
Therefore, the joint velocity of the two blocks after the collision is 0.8 m/s.
To calculate the joint velocity of the blocks after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Momentum (p) is calculated by multiplying an object's mass (m) by its velocity (v):
p = m * v
Let's first calculate the total momentum before the collision. The momentum of the first block (m1) moving with velocity (v1) is:
p1 = m1 * v1
Given that the mass of the first block (m1) is 0.1 kg and its velocity (v1) is 0.4 m/s, we can calculate its momentum (p1).
p1 = 0.1 kg * 0.4 m/s = 0.04 kg·m/s
Similarly, the momentum of the second block (m2) moving with velocity (v2) is:
p2 = m2 * v2
Given that the mass of the second block (m2) is 0.2 kg and its velocity (v2) is 1 m/s, we can calculate its momentum (p2).
p2 = 0.2 kg * 1 m/s = 0.2 kg·m/s
Now, let's find the total initial momentum before the collision by summing up the individual momenta of the blocks:
Initial Total Momentum = p1 + p2
Initial Total Momentum = 0.04 kg·m/s + 0.2 kg·m/s
Initial Total Momentum = 0.24 kg·m/s
According to the conservation of momentum, the total momentum after the collision should be equal to the initial total momentum.
Total Momentum after Collision = Initial Total Momentum
Total Momentum after Collision = 0.24 kg·m/s
Since the blocks stick together after the collision, their masses are combined, and let's call it M.
M = m1 + m2
M = 0.1 kg + 0.2 kg
M = 0.3 kg
Now, we can calculate the joint velocity after the collision by dividing the total momentum after the collision by the combined mass of the blocks.
Joint Velocity after Collision = Total Momentum after Collision / Combined Mass
Joint Velocity after Collision = 0.24 kg·m/s / 0.3 kg
Joint Velocity after Collision = 0.8 m/s
Therefore, the joint velocity of the blocks after the collision is 0.8 m/s.
since you give no information as to their directions, I will assume they are traveling in opposite directions.
So, if the .1kg mass is moving in the + direction, we have
0.1*0.4 - 0.2*1.0 = (0.1+0.2)v
v = -8/15