What is the Volcanic Intrusion "rule"-
1 answer:
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Answer:
Velocity of the two balls after collision: .
of kinetic energy would be lost.
Explanation:
<h3>Velocity</h3>Because the question asked about energy, convert all units to standard units to keep the calculation simple:
- Mass of the first ball:
.
- Mass of the second ball:
.
The two balls stick to each other after the collision. In other words, this collision is a perfectly inelastic collision. Kinetic energy will not be conserved. The velocity of the two balls after the collision can only be found using the conservation of momentum.
Assume that the system of the two balls is isolated. Thus, the sum of the momentum of the two balls will stay the same before and after the collision.
The momentum of an object of mass and velocity
is:
.
Momentum of the two balls before collision:
- First ball:
.
- Second ball:
.
- Sum:
given that the two balls are moving in the same direction.
Based on the assumptions, the sum of the momentum of the two balls after collision should also be . The mass of the two balls, combined, is
. Let the velocity of the two balls after the collision
. (There's only one velocity because the collision had sticked the two balls to each other.)
- Momentum after the collision from
:
.
- Momentum after the collision from the conservation of momentum:
.
These two values are supposed to describe the same quantity: the sum of the momentum of the two balls after the collision. They should be equal to each other. That gives the equation about :
.
.
In other words, the velocity of the two balls right after the collision should be .
The kinetic energy of an object of mass and velocity
is
.
Kinetic energy before the collision:
- First ball:
.
- Second ball:
.
- Sum:
.
The two balls stick to each other after the collision. Therefore, consider them as a single object when calculating the sum of their kinetic energies.
- Mass of the two balls, combined:
.
- Velocity of the two balls right after the collision:
.
Sum of the kinetic energies of the two balls right after the collision:
.
Therefore, of kinetic energy would be lost during this collision.
The momentum, p, of any object having mass m and the velocity v is
Let and
be the masses of the large truck and the car respectively, and
and V_S be the velocities of the large truck and the car respectively.
So, by using equation (i),
the momentum of the large truck
and the momentum of the small car .
If the large truck has the same momentum as a small car, then the condition is
The equation (ii) can be rearranged as
So, the first scenario:
So, to have the same momentum, the ratio of mass of truck to the mass of the car must be equal to the ratio of velocity of the car to the velocity of the truck.
The other scenario:
So, to have the same momentum, the ratio of mass of truck to the velocity of the car must be equal to the ratio of mass of the car to the velocity of the truck.