2. A particle of mass m and speed v collides at right angles with a very massive wall in a perfectly elastic collision. The magnitude of the change of momentum of the particle is
a.) zero
b.) mv/2
c.) mv
d.) �ã (2) mv
e.) 2mv
Hint: the final momentum is equal in magnitude and opposite in direction. Calculate the change.
If you have no idea what the answer is, you'd be better off reading about momentum than posting questions here.
Well, isn't this a smashing question! Let's tackle it.
In a perfectly elastic collision, the kinetic energy is conserved. Now, since the particle collides with a very massive wall, we can assume that the wall doesn't move or change its speed. This means that the change in momentum solely depends on the particle itself.
Since the particle collides at right angles with the wall, its velocity in the direction perpendicular to the wall will reverse while the velocity in the parallel direction remains the same. So, the change in momentum will be equal to the initial momentum of the particle.
Now, the initial momentum can be calculated as the product of mass and velocity, which gives us mv. Therefore, the magnitude of the change in momentum is mv, so the answer is c.) mv.
But hey, don't be discouraged if you didn't know the answer. It's always good to learn new things, and momentum is definitely an important concept to understand.
In a perfectly elastic collision, the total momentum of the system is conserved.
The initial momentum of the particle is given by m * v, where m is the mass of the particle and v is its initial velocity.
When the particle collides with the wall at right angles, its direction reverses and its final velocity becomes -v. Therefore, the final momentum of the particle is -m * v.
The change in momentum is given by the difference between the initial and final momentum of the particle, which is:
Change in momentum = final momentum - initial momentum
= (-m * v) - (m * v)
= -2mv
Therefore, the magnitude of the change in momentum of the particle is 2mv.
The correct answer is e.) 2mv.
To find the magnitude of the change in momentum during the collision, we need to consider 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.
In this case, the particle collides with a very massive wall, which we can assume is stationary. Since the wall is very massive compared to the particle, we can neglect its motion and consider it to be at rest.
Before the collision, the particle has an initial momentum given by p_initial = m * v, where m is the mass of the particle and v is its speed.
After the collision, the particle bounces back with the same speed but in the opposite direction. Therefore, the final momentum of the particle is given by p_final = -m * v, where the negative sign indicates the change in direction.
To find the change in momentum, we can subtract the initial momentum from the final momentum: Δp = p_final - p_initial = (-m * v) - (m * v) = -2m * v.
The magnitude of the change in momentum is given by |Δp| = | -2m * v | = |-2m * v | = 2m * v.
Thus, the correct answer is e.) 2mv. The magnitude of the change in momentum is equal to 2 times the mass of the particle multiplied by its speed.