Shanika is an engineer at an amusement park who is experimenting with changes to the setup for a magnetic roller coaster ride. I
n one ride, there are two identical roller coaster cars (orange and green) that start on opposite sides of a large magnet located at the center of a station. Shanika wants to get the largest increase in potential energy she can by moving one car one space to the left or the right.
Shanika can move the orange car to point A or point B, or she can move the green car to point C or point D. Which movement should she make? Why will that movement result in the largest increase in potential energy? Describe the magnetic force that will act on the roller coaster car she moves.
Shanika can move the orange car to point A or point B, or she can move the green car to point C or point D. Which movement should she make? Why will that movement result in the largest increase in potential energy? Describe the magnetic force that will act on the roller coaster car she moves.
1 answer:
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Answer:
The final speed for the mass 2m is and the final speed for the mass 9m is
.
The angle at which the particle 9m is scattered is with respect to the - y axis.
Explanation:
In an elastic collision the total linear momentum and the total kinetic energy is conserved.
<u>Conservation of linear momentum:</u>
Because the linear momentum is a vector quantity we consider the conservation of the components of momentum in the x and y axis.
The subindex 1 will refer to the particle 9m and the subindex 2 will refer to the particle 2m
In the x axis before the collision we have
and after the collision we have that
In the y axis before the collision
after the collision we have that
so
then
<u>Conservation of kinetic energy:</u>
so
Putting in one side of the equation each speed we get
We know that the particle 2m travels in the -y axis because it was stated in the question.
Now we can get the y component of the speed of the 9m particle:
the magnitude of the final speed of the particle 9m is
The tangent that the speed of the particle 9m makes with the -y axis is
As a vector the speed of the particle 9m is:
As a vector the speed of the particle 2m is:
Answer:
The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball.
Explanation:
In inelastic collision, the total momentum is always conserved after collision but the kinetic energy is reduced.
Momentum is Mass X velocity.
5 kg ball is in motion, while 10 kg ball is stationary; that is zero velocity.
The momentum of 10 kg ball before collision is zero while the momentum of 5 kg ball before collision is more than zero. Therefore, the magnitude of change in momentum will not be equal.
Next possible options are in kinetic Energy
Initial Kinetic energy =
Final kinetic energy =
Change in kinetic energy = Final Kinetic Energy - Initial Kinetic Energy
Change in kinetic energy of 5kg ball =
Since the 5-kg ball has initial velocity (u), the magnitude of the change in velocity will be reduced.
Change in kinetic energy of 10kg ball:
the ball is initially at rest, therefore the initial velocity (u) will be zero (0)
Δ K.E =
From the solution above, the magnitude of the change in velocity experienced by 10 kg ball is higher than 5 kg ball.
Hence, The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball