8/6/2019 PHYF144 C15

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Rosmiza Mokhtar, ESM Dept, COE, UNITEN

Exercise Chapter 5[Reminder : Calculator must be in Radian Mode if the angle is in radian]

1. The piston in an engine oscillates with SHM so that its displacement varies according to theexpression y = (10.0 cm) cos (2t + / 6) where y is cm and t is in s. At t = 0, find(a) the displacement of the particle, [8.66 cm]

(b) its velocity and [-10 cm/s] (c) its acceleration, [-34.6 cm/s 2] (d) find the period and amplitude of the motion. [T = s, A = 10 cm]

2. The displacement of a particle at t = 2.0 s is given by the expressionx = (5.00 cm) cos (4.00 t + ) where x is in cm and t is in s.

Determine(a) the frequency and the period of the motion, [f = 2 Hz, T = 0.5 s] (b) the amplitude of the motion, [A = 5 cm] (c) the phase constant and [ rad]

(d) the displacement at t = 2.0 s. [ x = 0]

3. An object moves along the y axis in SHM starts from equilibrium position at the origin at t = 0 andmoves upward (positive y). The amplitude of its motion is 2.00 cm and the frequency is 1.50 Hz.(a) Write down the equation of its displacement as a function of time.

[y = (2cm) sin (3 t) or y = (2cm) cos (3 t - /2)](b) Determine the maximum speed and the earliest time (after t = 0) at which this object has this

speed. [vmax = 6 cm/s, t = 0.333 s] (c) The maximum acceleration and the earliest time (after t = 0) at which this object has this

acceleration. [amax = 177.7 cm/s 2, t = 0.167 s]

4. A block of mass m is attached to a spring with spring constant 8.00 N/m and undergoes SHM withan amplitude 10.0 cm. When the mass is halfway between its equilibrium position and end point,its speed is + 20 cm/s. Calculate(a) the mass, m [m = 1.5 kg] (b) period of the motion and [T = 2.72 s] (c) them maximum acceleration. [amax = 0.533 m/s 2]

5. A 0.500-kg cube connected to a light spring for which the force constant is 20.0 N/m oscillates on ahorizontal, frictionless track.(a) Calculate the total energy of the system and the maximum speed of the cube if the amplitude

of the motion is 3.00 cm, [9.00 10 -3 J] (b) What is the velocity of the cube when the displacement is 2.00 cm? [ 0.141 m/s] (c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm.

[K = 5.00 10 -3 J, U = 4.00 10 -3 J](d) For what values of x is the speed of the cube 0.100 m/s? [ 2.55 cm]

8/6/2019 PHYF144 C15

http://slidepdf.com/reader/full/phyf144-c15 2/2

Rosmiza Mokhtar, ESM Dept, COE, UNITEN

6. A 100-g mass is connected to a spring with a force constant of 20.0 N/m oscillates on a horizontal,frictionless surface with amplitude of 6.00 cm. Find(a) the total energy of the system, [36 mJ] (b) the speed of the mass when the displacement is 1.5 cm, [0.82 m/s] (c) the kinetic energy, and [11 mJ]

(d) the potential energy when the displacement is 5.00 cm. [25 mJ]

7. A 0.5-kg mass attached to a spring with a force constant 10.0 Nm -1 vibrates in SHM on a horizontalfrictionless surface. The spring is compressed by 2.00 cm (x = -2.00 cm). The mass is released fromrest. Find(a) the period of its motion [T = 1.40 s] (b) the maximum values of its speed and acceleration [vmax = 0.0894 m/s, a max = 0.40 m/s 2] (c) the displacement, velocity and acceleration as function of time.

[x = (-2cm) cos (4.47 t), v = (8.94 cm/s) sin (4.47 t), a = (40 cm/s 2) cos (4.47 t)]

8. A 2.00-kg mass at rest on a surface is attached to a horizontal spring having a force constant 20Nm -1. The spring initially is unstretched. Then a constant horizontal force 30.0 N is applied to themass. Determine the speed of the mass after it moved 0.4 m from the equilibrium position[assumed the surface and the mass has no friction]. [v = 3.22 m/s]If the coefficient of kinetic friction between the mass and the surface is 0.20, what is its speed?[2.97 m/s]

9. A simple pendulum is 5.00 m long.(a) What is the period of SHM for this pendulum if it is hang in an elevator that is acceleratingupward at 3.00 ms -2? [T = 3.93 s] (b) what is the period of SHM if the elevator is accelerating downward at 3.00 ms -2? [T = 5.39 s]

10. A simple pendulum has a mass of 0.3 kg and a length of 1.5 m. It is displaced by an angle 10.0 o and then released. What is(a) the maximum speed, [vmax = 0.668 m/s] (b) the maximum angular acceleration, [ = 1.135 rad/s 2] (c) the maximum restoring force [0.51 N] .