Answer:
Part a)
Part b)
Part c)
distance L is independent of the mass of the sphere
Explanation:
Part a)
As we know that rotational kinetic energy of the sphere is given as
so we will have
so we will have
Part b)
By mechanical energy conservation law we know that
Work done against gravity = initial kinetic energy of the sphere
So we will have
Part c)
by equation of energy conservation we know that
so here we can see that distance L is independent of the mass of the sphere
Answer:
D.) 1m/s
Explanation:
Assume the initial angle of the swing is 12.8 degree with respect to the vertical. We can calculate the vertical distance from this initial point to the lowest point by first calculate the vertical distance from this point the the pivot point:
where L is the pendulum length
The vertical distance from the lowest point to the pivot point is the pendulum length 2m
this means the vertical distance from this initial point to the lowest point is simply:
As the pendulum travel (vertically) from the initial point to the bottom point, its potential energy is converted to kinetic energy:
where m is the mass of the pendulum, g = 10 m/s2 is the constant gravitational acceleration, h = 0.05 is the vertical it travels, v is the pendulum velocity at the bottom, which we are trying to solve for.
The m on both sides of the equation cancel out
so D is the correct answer
