A 1.2-kg blob of putty moving at 4.0m/s slams into a 1.2-kg blob of putty at rest. Calculate the speed of the two stuck-together blobs of putty immediately after colliding.
Express your answer to two significant figures and include the appropriate units.
momentum before = momentum after
1.2 * 4 = 2.4 * v
To calculate the speed of the two stuck-together blobs of putty immediately after the collision, we can use the conservation of momentum principle.
The conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces act on the system.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
For the first blob of putty moving at 4.0 m/s, its momentum before the collision can be calculated as:
p1 = (mass1) * (velocity1)
= (1.2 kg) * (4.0 m/s)
For the second blob of putty at rest, its momentum before the collision is zero since its velocity is zero:
p2 = (mass2) * (velocity2)
= (1.2 kg) * 0
= 0
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. Therefore:
p1 + p2 = p(total after collision)
(1.2 kg) * (4.0 m/s) + 0 = (total mass) * (velocity after collision)
We know that the two blobs of putty stick together after the collision, so their total mass is calculated by adding the individual masses:
total mass = (mass1) + (mass2)
= (1.2 kg) + (1.2 kg)
= 2.4 kg
Substituting the values into the equation:
(1.2 kg) * (4.0 m/s) + 0 = (2.4 kg) * (velocity after collision)
(4.8 kg∙m/s) = (2.4 kg) * (velocity after collision)
To find the velocity after the collision, divide both sides of the equation by the total mass (2.4 kg):
velocity after collision = (4.8 kg∙m/s) / (2.4 kg)
= 2.0 m/s
Therefore, the speed of the two stuck-together blobs of putty immediately after colliding is 2.0 m/s (rounded to two significant figures), and the unit is meters per second (m/s).