All analysis is to be kept general and given in your solutions. Only substitute

Question

All analysis is to be kept general and given in your solutions. Only substitute in the numerical values at the end of the derivation when necessary and state all assumptions and any principles of dynamics applied, choice of coordinate systems, etc. Where necessary use g 9.81 ms-2. A new game comprises a mass of 0.25 kg attached by an elastic cord to a fixed point 0. It moves on a horizontal surface and the aim is to hit the mass so that it will fall into an inner circle, where due to the surface being rough the mass will slow down and stop. Outside of the inner circle the surface is frictionless. It is assumed that the elastic cord will only store energy and apply a force on the mass when it is stretched from its original length. A schematic of the game when the ball is at a position outside of the inner circle is given in Figure 1 below. Positive direction for moments Figure 1: A mass moving with velocity uA at position A 30 cm from 0 as shown. The inner radius R is equal to 20 cm, the unstretched length of the elastic cord L is also 20 cm and the stiffness k of the elastic cord when extended is 1500 N/m. The initial velocity of the mass uA is equal to 1 m/s when it is struck by a bat which applies an impulse of 0.5 Ns to the mass in the positive y direction. Length OA is 30 cm. (a)(i) Determine the new velocity of the mass immediately after the impulse has been applied. (ii) What is the gain in the kinetic energy of the mass due to the application of the impulse? (b) The mass then travels on a curved path (AB) under the action of the stretched cord. [5 marks] [6 marks] (i) Using the Work-Energy principle or Conservation of Energy, determine the velocity of the mass when it enters the inner circle at point B. [7 marks] (ii) Using the Conservation of Angular Momentum about O between points A and B, find the distance between O and C. Why can one use the Conservation of Angular Momentum to determine the closest distance? [6 marks] (c) The coefficient of sliding friction k inside the inner circle is equal to 0.8. As the mass slides on the path between points B and D the friction force provides a constant moment about the point O. Determine whether the mass will exit the circle at point D. [10 marks] FEEG1002 Dynamics Assignment 2 (2016/17) (d) The game proves unpopular as it is very difficult to ‘land’ the mass into the inner circle. Describe what effect the following changes might make on the dynamics of the mass and whether the game would be more likely to be playable given the same initial conditions and applied impulse. (i) Making the surface of the mass rougher, (ii) increasing the mass from 0.25 kg or (iii) making the cord inextensible and of length 30 cm with the same initial conditions of the mass velocity as in (a)(i) after the impulse has been applied. [6 marks]

Explanation / Answer

from the given question,

mass (m)=0.25 kg

initial velocity(u)=1 m/s

Impulse=0.5Ns

(i) Impulse = change in momentum

Impulse= m(v-u)

0.5=0.25(v-1)

2=v-1

v=3m/s

new velocity of mass = 3m/s

(ii)Gain in kinetic energy= 1/2 m (v2-u2)

=1/2 (0.25) (32-12)

=1J

Gain in kinetic energy is 1 Joule.

(iii) Using conservation of energy

The initial extension of cord is 10cm

1/2 mv2 + 1/2 kx2 = 1/2 mv2

(0.25)(32)+ (1500)(0.1)2=v2

v=4.15m/s

(iv) Angular momentum at A = Angular momentum at B =Angular momentum at C

m(3)0.3=m(4.15)(r)

r=0.216m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.