SCIENCE
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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:
Here we have mass that moves at ceratin speed. This means that we have momentum. The law that must be observed is law of conservation of momentum. It states that momentum before certain event is equal to a momentum after that event. Here we have three masses so we can write this as:
Before the firecracker blows a coconut does not move, so left side is equal to 0:
We know that m1=m2=m and m3=2m. Also we are asked to find v3f so we can rewrite formula:
We must take in consideration that two parts with same mass do not move in same direction. The center of mass of these two parts moves between them at angle of 45° with respect to both south and west. The speed of a center of mass is:
This speed we can insert into formula for v3f:
We can see that part of a coconut with biggest mass has same speed as center of mass of two other parts. Negative sign shows that direction is opposite to direction of two pats. Biggest part moves towards north-east.
Before the firecracker blows a coconut does not move, so left side is equal to 0:
We know that m1=m2=m and m3=2m. Also we are asked to find v3f so we can rewrite formula:
We must take in consideration that two parts with same mass do not move in same direction. The center of mass of these two parts moves between them at angle of 45° with respect to both south and west. The speed of a center of mass is:
This speed we can insert into formula for v3f:
We can see that part of a coconut with biggest mass has same speed as center of mass of two other parts. Negative sign shows that direction is opposite to direction of two pats. Biggest part moves towards north-east.