Question 1 (30 P): A pendulum has a length l (the rope has no mass). The mass of the object
suspended from the pendulum is m . Ip with horizontal θ = 90 o
When it makes an angle of degrees, we first leave the object at no speed. Any friction can be
neglected. Gravitational acceleration
g . Give your answers in terms of l , m and g .
(a) (15 P) Pendulum lowermost point ( θ = 0 o ) What Is when the speed?
(b) (15 P) θ = 0 o when there is, what is the strand tension?
Question 2 (70 P): An apple of mass m rotates at a constant speed in a horizontal plane, attached to a
rope. Α angle with rope vertical
(see figure). Radius of the circle R is. One complete turn of the apple takes τ seconds. Direction of
rotation
indicated in the figure. Apple is approaching you at the S point. Q is the center of the circle. QP is
the vertical distance. SQ plus
In the x direction, QP is in the y direction and the z direction is tangent to the circle at
point S and towards you. Gravitational acceleration
g . Suppose the rope has no mass. Give your answers in terms of m , R , τ and g .
(a) (10 P) Draw the free body diagram at point S for apple .
(b) (15 P) S rate from apples and ω definition of magnitude as the angular velocity?
(c) (15 P) What is the centripetal acceleration (in magnitude and direction ) of the apple at point S ?
(d) (15 P) What is the direction and magnitude of the sum of all forces acting on the apple at point S ?
(e) (15 P) What is the angle α ?