# Solving for Velocity: Elastic Collision of Two Balls with Different Mass in m/s

• drkidd22
In summary, the velocity in an elastic collision is calculated using the equation: v = (m1 * u1 + m2 * u2) / (m1 + m2), where m1 and m2 are the masses of the objects and u1 and u2 are their initial velocities. The velocity of an object can change during an elastic collision in order to conserve momentum. An elastic collision differs from an inelastic collision in that kinetic energy is conserved in addition to momentum. The mass of an object indirectly affects its velocity in an elastic collision. And finally, it is possible for an object's velocity to increase after an elastic collision, especially if it collides with a larger object.
drkidd22
One ball traveling at 17.7 m/s strikes a second ball at rest in an elastic collision. If the mass of the first ball is 30 kg and the mass of the second is 1.2 kg, to the nearest tenth of a m/s what is the velocity of the first ball after the collision?

## Homework Equations

you need a 2nd eq, conservation of momentum.

:

In an elastic collision, the total momentum and kinetic energy of the system are conserved. This means that the total momentum before the collision is equal to the total momentum after the collision, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Using the conservation of momentum equation, we can solve for the final velocity of the first ball (v1f) after the collision:

m1v1i + m2v2i = m1v1f + m2v2f

Where:
m1 = mass of first ball (30 kg)
v1i = initial velocity of first ball (17.7 m/s)
m2 = mass of second ball (1.2 kg)
v2i = initial velocity of second ball (0 m/s)
v2f = final velocity of second ball (unknown)
v1f = final velocity of first ball (unknown)

We can solve for v1f by rearranging the equation:

v1f = (m1v1i + m2v2i - m2v2f)/m1

Plugging in the given values, we get:

v1f = (30 kg)(17.7 m/s) + (1.2 kg)(0 m/s) - (1.2 kg)(v2f)/30 kg
v1f = 531 kg•m/s - 1.2 kg•m/s - (1.2 kg)(v2f)/30 kg
v1f = 529.8 kg•m/s - (1.2 kg)(v2f)/30 kg

Next, we use the conservation of kinetic energy equation to solve for v2f:

(m1v1i^2 + m2v2i^2) = (m1v1f^2 + m2v2f^2)

Plugging in the given values, we get:

(30 kg)(17.7 m/s)^2 + (1.2 kg)(0 m/s)^2 = (30 kg)(v1f)^2 + (1.2 kg)(v2f)^2
9438 kg•m^2/s^2 = 900 kg•m^2/s^2 + (1.2 kg)(v2f)^2
9438 kg•m^2/s^2 - 900 kg•m^2/s^2 = (

## 1. How is velocity calculated in an elastic collision?

In an elastic collision, the velocity is calculated using the equation: v = (m1 * u1 + m2 * u2) / (m1 + m2), where m1 and m2 are the masses of the two objects and u1 and u2 are their initial velocities.

## 2. Can the velocity of an object change during an elastic collision?

Yes, the velocity of an object can change during an elastic collision. This is because the total momentum of the system remains constant, but the individual velocities of the objects can change in order to conserve momentum.

## 3. What is the difference between an elastic and an inelastic collision?

In an elastic collision, both the kinetic energy and momentum of the system are conserved, while in an inelastic collision, only momentum is conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

## 4. How does the mass of an object affect its velocity in an elastic collision?

In an elastic collision, the mass of an object does not directly affect its velocity. However, the mass does affect the momentum of the object, which in turn can affect its velocity. Objects with larger masses will have a greater momentum and therefore may have a different velocity after the collision compared to objects with smaller masses.

## 5. Can the velocity of an object after an elastic collision be greater than its initial velocity?

Yes, it is possible for the velocity of an object after an elastic collision to be greater than its initial velocity. This can occur if the object collides with another object of a much larger mass, causing the smaller object to gain a higher velocity in order to conserve momentum.

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