A 3.0-kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M?
5 kg
answer is 5.12
To find the mass of the object (M) after the collision, we can use the conservation of momentum principle. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Before the collision:
The momentum of the 3.0 kg object is given by:
P1 = (3.0 kg) * (8.0 m/s) = 24 kg·m/s
Since the second object is initially at rest, its momentum is zero:
P2 = 0 kg·m/s
After the collision:
The mass of the object is now M, and its velocity is 6.0 m/s:
P1' = (M kg) * (6.0 m/s) = 6M kg·m/s
The momentum is conserved, so we can set the initial momentum equal to the final momentum:
P1 + P2 = P1'
24 kg·m/s + 0 kg·m/s = 6M kg·m/s
Simplifying the equation:
24 kg·m/s = 6M kg·m/s
Dividing both sides of the equation by 6 kg·m/s:
M = 24 kg·m/s / 6 kg·m/s = 4 kg
Therefore, the mass (M) of the object after the collision is 4 kg.
To find the mass of the unknown object (M), we can use the principles of conservation of momentum and kinetic energy in an elastic collision. Here's how you can calculate the value of M:
1. Begin by finding the initial momentum of the system:
Momentum = mass × velocity
The initial momentum of the 3.0-kg object is given by:
Momentum_initial = mass_initial × velocity_initial
Since the initial velocity of the 3.0-kg object is 8.0 m/s and it is moving in the positive x direction, we have:
Momentum_initial = 3.0 kg × 8.0 m/s
2. Next, determine the final momentum of the system after the collision:
Momentum = mass × velocity
The final momentum of the unknown object is given by:
Momentum_final = mass_final × velocity_final
Since the final velocity of the unknown object is 6.0 m/s and it is moving in the positive x direction, we have:
Momentum_final = M × 6.0 m/s
3. Apply the conservation of momentum principle:
According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Therefore, we can equate the initial momentum to the final momentum:
Momentum_initial = Momentum_final
Substituting the values we obtained from steps 1 and 2, we get:
3.0 kg × 8.0 m/s = M × 6.0 m/s
4. Solve for M:
Now we can solve for M by rearranging the equation:
M = (3.0 kg × 8.0 m/s) / (6.0 m/s)
Simplifying the expression, we have:
M = 4.0 kg
Therefore, the mass of the unknown object (M) is 4.0 kg.