Why doesnt a ball roll on forever after being kicked at a soccer game
1 answer:
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Answer:
a) see attached, a = g sin θ
b)
c) v = √(2gL (1-cos θ))
Explanation:
In the attached we can see the forces on the sphere, which are the attention of the bar that is perpendicular to the movement and the weight of the sphere that is vertical at all times. To solve this problem, a reference system is created with one axis parallel to the bar and the other perpendicular to the rod, the weight of decomposing in this reference system and the linear acceleration is given by
Wₓ = m a
W sin θ = m a
a = g sin θ
b) The diagram is the same, the only thing that changes is the angle that is less
θ' = 9/2 θ
c) At this point the weight and the force of the bar are in the same line of action, so that at linear acceleration it is zero, even when the pendulum has velocity v, so it follows its path.
The easiest way to find linear speed is to use conservation of energy
Highest point
Em₀ = mg h = mg L (1-cos tea)
Lowest point
Emf = K = ½ m v²
Em₀ = Emf
g L (1-cos θ) = v² / 2
v = √(2gL (1-cos θ))
Answer:
Explanation:
First of all, let's remind that:
- The kinetic energy of an object is given by , where m is the mass and v is the speed
- The momentum of an object is given by
- The inertia of an object is proportional to its mass, so we can write , where k just indicates a constant of proportionality
In this problem, we have:
- (the two objects have same kinetic energy)
- (A has three times the momentum of B)
Re-writing both equation we have:
If we divide first equation by second one we get
And if we substitute it into the first equation we get
So, B has 9 times more mass than A, and so B has 9 times more inertia than A, and their ratio is: