Answer:
Explanation:
The acceleration of the block can be found by the kinematics equations:
Since the plane is frictionless, the only force acting on the block along the motion of the block is its weight.
To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as
As M=m, then
Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then
Therefore replacing we have that,
Re-arrange to find v,
Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that
Therefore
Therefore the velocity when they are about to collide is
Answer:
0.75 m
Explanation:
Let's call the distance between the bulb and the mirror x.
The bulb and the length of the mirror form a triangle. The mirror and the illuminated area on the floor form a trapezoid. If we extend the lines from the mirror edge to the reflected image of the bulb, we turn that trapezoid into a large triangle. This triangle and the small triangle are similar. So we can say:
x / 0.4 = (3 + x) / 2
Solving for x:
2x = 0.4 (3 + x)
2x = 1.2 + 0.4 x
1.6 x = 1.2
x = 0.75
So the bulb should located no more than 0.75 m from the mirror.
Answer: To increase the rigidity of the system you could hold the ruler at its midpoint so that the part of the ruler that oscillates is half as long as in the original experiment.
Explanation:
When a rule is displaced from its vertical position, it oscillates back and forth because of the restoring force opposing the displacement. That is, when the rule is on the left there is a force to the right.
By holding a ruler with one hand and deforming it with the other a force is generated in the opposite direction which is known as the restoring force. The restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero. The momentum gained causes the ruler to move to the right leading to opposite deformation. This moves the ruler again to the left. The whole process is repeated until dissipative forces reduce the motion causing the ruler to come to rest.
The relationship between restoring force and displacement was described by Hooke's law. This states that displacement or deformation is directly proportional to the deforming force applied.
F= -kx, where,
F= restoring force
x= displacement or deformation
k= constant related to the rigidity of the system.
Therefore, the larger the force constant, the greater the restoring force, and the stiffer the system.
elasticity stretches and can also return to it's normal size ..