# Newtons Law, Rotational Motion and Simple Harmonic Motion

A horizontal force of 50 N acts on a mass of 6 kg resting on a horizontal surface. The mass is initially at rest and covers a distance of 5 m O.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant:

(a) Calculate the total energy expended in the acceleration.

(b) Plot a graph of the kinetic energy of the mass against time.

(c) Plot a graph of the kinetic energy of the mass against distance.

(d) Calculate the coefficient of friction between the mass and the surface.

A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2 (attached). If the mass is released from rest and falls a distance of 0.5 m in 1.5 s, calculate:

(a) The linear acesleration of the mass.

(b) The angular acceleration of the wheel.

(c) The tension in the rope.

(d) The frictional torque, resisting motion.

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration, calculate:

(a) (i) the frequency of vibration

(ii) the maximum velocity of the mass during the vibration

(ii) the maximum acceleration of the mass during the vibration

(iv) the mass required to produce double the maximum velocity calculated in (ii) using the same spring and initial deflection.

(b) Plot a graph of acceleration against displacemmt (x) (for values of from:. -10 mm to = .10 mm)