Which of the following statements best describes the characteristic of the restoring force in the spring-mass system described i
2 answers:
Answer : The restoring force is directly proportional to the displacement of the block.
Explanation :
Restoring force is defined as the force that is exerted by the spring due to its mass.
Mathematically, the restoring force can be written as :
F = - k x
where,
k is the spring constant.
x is the displacement caused due to the mass.
Negative sign shows that the force is acting in opposite direction.
So, it is clear that the restoring force is directly proportional to the displacement of the block.
Hence, the correct option is (b) " The restoring force is directly proportional to the displacement of the block ".
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Answer:
Explanation:
using the law of the conservation of the linear momentum:
where is the inicial momemtum and
is the final momentum
the linear momentum is calculated by the next equation
P = MV
where M is the mass and V is the velocity.
so:
where m is the mass of the proton and is the velocity of the proton after the collision,
is the mass of the nucleus and
is the velocity of the nucleus after the collision.
therefore, we can formulate the following equation:
m(270 m/s) = m + 14m
then, m is cancelated and we have:
270 = +
This is a elastic collision, so the kinetic energy K is conservated. Then:
and
Kf =
then,
=
here we can cancel the m and get:
=
now, we have two equations and two incognites:
270 = +
(eq. 1)
=
in the second equation, we have:
36450 = (eq. 2)
from this last equation we solve for as:
and replace in the other equation as:
270 = 14
so,
Vp is negative because the proton go in the -i hat direction.
Finally, replacing this value on eq. 1 we get: