A 10g object moving to the right at 20cm/s makes an elastic head-on collision with a 15g object moving in the opposite at 30cm/s. Find the velocity of each object after the collision.
answer: -40cm/s, 10cm/s
Assume both total momentum and total kinetic energy are conserved, and that the recoil velocities are along the same axis.
I will be glad to critique your work.
Object A of mass 20kg moving with velocity of 3m/s makes a head collition wth an object B of mass 10kg moving wth a velocity of 2m/s in opposite directinn. If a&b stick together after collision,caculate their common velocity v in the direction of A
To find the velocities of each object after the 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 total momentum before the collision can be calculated by adding the momentum of each object:
Momentum1 = mass1 * velocity1
Momentum2 = mass2 * velocity2
Given:
mass1 = 10g = 0.01kg
velocity1 = 20cm/s = 0.20m/s
mass2 = 15g = 0.015kg
velocity2 = -30cm/s = -0.30m/s (since it is moving in the opposite direction)
Now, calculate the total momentum before the collision:
Total momentum before collision = Momentum1 + Momentum2
= (mass1 * velocity1) + (mass2 * velocity2)
= (0.01kg * 0.20m/s) + (0.015kg * (-0.30m/s))
= 0.002kg·m/s + (-0.0045kg·m/s)
= -0.0025kg·m/s
Since the collision is elastic, the total momentum after the collision will be the same as the total momentum before the collision.
Total momentum after collision = -0.0025kg·m/s
Now, let's assume the velocities of the objects after the collision as V1 and V2.
Total momentum after the collision = (mass1 * V1) + (mass2 * V2)
= (0.01kg * V1) + (0.015kg * V2)
= -0.0025kg·m/s
We also know that the two objects are moving in opposite directions. Therefore, we can write the equation for the total momentum after the collision as:
Total momentum after collision = (mass1 * V1) - (mass2 * V2)
Setting the two equations equal to each other, we have:
-0.0025kg·m/s = (0.01kg * V1) + (0.015kg * V2)
Now, we need to solve these two equations simultaneously to find the velocities V1 and V2.
By rearranging the equation, we have:
0.01kg * V1 + 0.015kg * V2 = -0.0025kg·m/s ------ (Equation 1)
We also know that the velocity of one object is the negative of the velocity of the other object since they move in opposite directions. Therefore:
V1 = -V2 ------ (Equation 2)
Substitute V1 = -V2 into Equation 1:
0.01kg * (-V2) + 0.015kg * V2 = -0.0025kg·m/s
-0.01kg * V2 + 0.015kg * V2 = -0.0025kg·m/s
0.005kg * V2 = -0.0025kg·m/s
V2 = (-0.0025kg·m/s) / (0.005kg)
V2 = -0.5m/s
Now substitute V2 = -0.5m/s into Equation 2:
V1 = -(-0.5m/s)
V1 = 0.5m/s
Therefore, the velocity of the 10g object after the collision is 0.5m/s to the right, and the velocity of the 15g object after the collision is -0.5m/s to the left.
In cm/s, the velocities are 50cm/s to the right and -50cm/s to the left.
So, the final answer is:
Velocity of the 10g object after the collision = 50cm/s to the right
Velocity of the 15g object after the collision = -50cm/s to the left
To find the velocities of each object after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
First, let's calculate the initial momentum and initial kinetic energy of the system.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v), so the initial momentum of the system is:
Initial momentum = (mass of object 1 * velocity of object 1) + (mass of object 2 * velocity of object 2)
Plugging in the given values:
Initial momentum = (10g * 20cm/s) + (15g * (-30cm/s))
Next, let's calculate the initial kinetic energy of the system. The kinetic energy (KE) of an object is given by half the product of its mass and the square of its velocity, so the initial kinetic energy of the system is:
Initial kinetic energy = (1/2 * mass of object 1 * (velocity of object 1)^2) + (1/2 * mass of object 2 * (velocity of object 2)^2)
Plugging in the given values:
Initial kinetic energy = (1/2 * 10g * (20cm/s)^2) + (1/2 * 15g * (30cm/s)^2)
Now, let's 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.
After the collision, the 10g object will be moving to the left, so its velocity will be negative (let's call it v1), and the 15g object will be moving to the right, so its velocity will be positive (let's call it v2).
Using the principle of conservation of momentum, we can write the equation:
Initial momentum = (mass of object 1 * velocity of object 1) + (mass of object 2 * velocity of object 2)
Plugging in the known values:
(10g * 20cm/s) + (15g * (-30cm/s)) = (10g * v1) + (15g * v2)
Next, let's use the principle of conservation of kinetic energy. According to this principle, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Using the equation for initial kinetic energy:
Initial kinetic energy = (1/2 * mass of object 1 * (velocity of object 1)^2) + (1/2 * mass of object 2 * (velocity of object 2)^2)
Plugging in the known values:
(1/2 * 10g * (20cm/s)^2) + (1/2 * 15g * (30cm/s)^2) = (1/2 * 10g * (v1)^2) + (1/2 * 15g * (v2)^2)
Finally, we have two equations with two unknowns (v1 and v2). We can solve these equations simultaneously to find the values of v1 and v2.