A body of mass 20kg moving with a velocity of 8m/s collides with a stationary body of mass 10kg and the two stick together.They then move with a common velocity V.Find the value of V.
conserve momentum
20*8 + 10*0 = (20+10)v
A solution to the question
To find the value of the common velocity (V) after the collision, we can use the principles of conservation of momentum.
According to the conservation of momentum, the total momentum of an isolated system remains constant before and after a collision.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is defined as:
p = m * v
Where:
p is the momentum,
m is the mass of the object,
v is the velocity of the object.
Before the collision, the 20 kg mass is moving with a velocity of 8 m/s, and the 10 kg mass is stationary (i.e., its velocity is 0 m/s).
Let's calculate the initial momentum of the system (before collision) using the formula mentioned above:
Initial momentum = (mass1 * velocity1) + (mass2 * velocity2)
= (20 kg * 8 m/s) + (10 kg * 0 m/s)
= 160 kg m/s + 0 kg m/s
= 160 kg m/s
Since the two bodies stick together after the collision, their masses combine, and they move together with a common velocity (V). Let the combined mass be M.
After the collision, the combined momentum can be calculated as:
Final momentum = M * V
According to the conservation of momentum, the initial momentum and final momentum should be equal:
Initial momentum = Final momentum
So, we have:
160 kg m/s = M * V
Now, considering the masses of the individual bodies:
M = mass1 + mass2
= 20 kg + 10 kg
= 30 kg
Substituting this value in the above equation, we get:
160 kg m/s = 30 kg * V
To find the value of V, we need to rearrange the equation as follows:
V = (160 kg m/s) / (30 kg)
= 5.33 m/s (rounded to two decimal places)
Therefore, the value of the common velocity (V) after the collision is approximately 5.33 m/s.