What is an invasive species plant??
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At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
. So we can write
that we can solve to find an expression for v:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
that we can solve to find an expression for v:
a) 32 kg m/s
Assuming the spring is initially at rest, the total momentum of the system before the collision is given only by the momentum of the bowling ball:
The ball bounces off at the same speed had before, but the new velocity has a negative sign (since the direction is opposite to the initial direction). So, the new momentum of the ball is:
The final momentum after the collision is the sum of the momenta of the ball and off the spring:
where is the momentum of the spring. For the conservation of momentum,
b) -32 kg m/s
The change in momentum of bowling ball is given by the difference between its final momentum and initial momentum:
c) 64 N
The change in momentum is equal to the product between the average force and the time of the interaction:
Since we know , we can find the magnitude of the force:
The negative sign simply means that the direction of the force is opposite to the initial direction of the ball.
d) The force calculated in the previous step (64 N) is larger than the force of 32 N.