The weight is pulled down a further 20 mm and released. Calculate: (i) the period of oscillation of the weight (ii) the maximum acceleration of the sphere
(iii) the velocity of the weight when the acceleration is at a maximum (iv) the frequency of oscillation of the weight. (Acceleration due to gravity 9.8 m s2.)
‘SECTION B’
HALF QUESTION Typical of Question 12 in Leaving Cert. Exam
Q4 Answer all of the following parts (a), (b) and (c).
(a) The equation F ks, where k is a constant, is an expression for a law that governs the motion of a body. Name this law and give a statement of it.
Explain the significance of the ‘’ in the equation F ks.
A system that obeys this law will undergo a certain type of motion. Name and describe this type of motion.
A weight oscillating up and down at the end of a stretched spring is an example of a system that obeys this law. Give two other examples of systems that obey this law.
(b) A 45 kg child compresses the springs of a pogo-stick by 35 mm when she stands on it. In order to bounce on the pogo-stick she applies a downward force that compresses the spring further. This causes the pogo-stick and the child to oscillate up and down.
Use Hooke’s law to calculate the value of k, the constant for the springs of the pogo-stick.
The total mass of the frame of the pogo-stick and the child is 80 kg. Calculate: (i) the period of oscillation of the child (ii) the frequency of oscillations of the child.
(c) A pendulum of length 40 cm is allowed to swing through a small angle of oscillation. Given that acceleration due to gravity 9.8 m s2, calculate: (i) the periodic time for that length pendulum (ii) the frequency of oscillations
(iii) the frequency if the length of the pendulum was increased fourfold. What would be the effect on the periodic time if the mass of the pendulum bob was doubled? (9)
