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:
Kinetic energy would increase by a factor of 4 where as momentum would increase by a factor of 2.
Explanation:
Kinetic Energy is given by 0.5*mass*velocity^2. Kinetic Energy is proportional to Velocity^2.
Momentum is given by mass*velocity. Momentum is proportional to Velocity.
If the velocity of an object is doubled, Kinetic energy would increase by a factor of 2^2 i.e 4 times. Momentum would increase by a factor of 2.
Y₀ = initial position of the balloon at the top of the building = 44 m
Y = final position of the balloon at halfway down the building = 44/2 = 22 m
a = acceleration of the balloon = - 9.8 m/s²
v₀ = initial velocity of the balloon = 0 m/s
v = final velocity of the balloon = ?
using the kinematics equation
v² = v₀² + 2 a (Y - Y₀)
inserting the values
v² = 0² + 2 (- 9.8) (22 - 44)
v = 20.78 m/s