MULUNGUSHI UNIVERSITY
PHY 102 Tutorial sheet 2
1.0 A 0.250 kg block attached to a light spring oscillates on a frictionless, horizontal table. The
oscillation amplitude is A = 0.125 m and the block moves at 3.00 m/s as it passes through
equilibrium at x = 0.
(a) Find the spring constant, k.
(b) Calculate the total energy of the block- spring system.
(c) Find the block’s speed when x = A/2.
2.0 A horizontal block-spring system with the block on a frictionless surface has total mechanical
energy E = 47.0 J and a maximum displacement from equilibrium of 0.240 m.
(a) What is the spring constant?
(b) What is the kinetic energy of the system at the equilibrium point?
(c) If the maximum speed of the block is 3.45 m/s, what is its mass?
(d) What is the speed of the block when its displacement is 0.160 m?
(e) Find the kinetic energy of the block at x = 0.160 m.
(f) Find the potential energy stored in the spring when x = 0.160 m.
(g) Suppose the same system is released from rest at x = 0.240 m on a rough surface so that it loses
14.0 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What
is its position at that instant?
3.0 A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is
applied. A 0.500 kg particle rests on a frictionless horizontal surface and is attached to the free
end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from
rest at t = 0.
(a) What is the force constant of the spring?
(b) What are the angular frequency ω, the frequency, and the period (T) of the motion?
(c) What is the amplitude of the motion?
(d) What are the maximum velocity and the maximum acceleration of the particle?
(e) What are the maximum velocity and the maximum acceleration of the particle?
(f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s.
(g) Determine the velocity and acceleration of the particle when t = 0.500 s.
4.0 (a) For a simple pendulum of length L and mass of the bob m, show that for small angles of
displacement, the pendulum undergoes Simple harmonic Motion.
(b) Show also that for a simple pendulum the period and frequency is given by
s
L
T = 2π
g
r
1
g
f=
2π L
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