MEC2405 Machine Dynamics

Assignment

Due Date: 9 May 2017

Value: 400 of the 1000 marks for this course

I estimate that students who are fully competent in the course material will take 4-5 hours to complete this assignment. Student learning as they do the assignment may take between 20-25.

Question 1 (50 marks)

A car travelling on level ground at a constant 100 km/h drives off a 20 m high cliff. Treating the car as a particle and ignoring any air resistance, calculate the: (i) time taken for the car to reach the bottom of the cliff;

(ii) horizontal distance travelled from the cliff edge to the point of impact; and (iii) the velocity immediately before impact.

A comparison with similar accidents indicates that treating the car as a particle is not entirely accurate. Describe the motion that you expect if the engine is at the front of the vehicle and explain why you decided this was the case.

Question 2 (50 marks)

A 10 kg block is placed on an inclined surface as shown in the following diagram. Determine its kinetic energy and momentum at the instant it has traveled 250 mm from its initial placement. The static coefficient of friction between the block and inclined surface is 0.28 and the kinetic coefficient of friction is 0.22.

Question 3 (80 marks)

The end of cable D, as shown in the following figure, is pulled off the bottom of the drum with a horizontal velocity of 40 mm/s causing the cylinder to roll without slipping. Determine: (i) the angular velocity of the drum

(ii) the absolute velocity of centre A

(iii) the absolute velocity of point P

Question 4 (80 marks)

A slotted disc rotates clockwise as it decelerates uniformly from 120 rpm to rest in 3.5 seconds. At the same time object A is moving 0.5 m/s outward in the slot at a rate of 0.5 m / s2.

Determine the nett acceleration of A at the instant the disc attains a speed of 30 rpm. The position of A at this instant in time is depicted in the following diagram.

Question 5 (140 marks)

Rod AO in the ‘cross trainer’ mechanism shown below is rotating clockwise at a constant 45 rpm. At the position and instant shown determine the:

(i) absolute velocity of each point - A, B, C, and D

(ii) angular velocity of link AB and link BC

(iii) acceleration point A

(iv) acceleration point B and the angular acceleration of arm BC

OA = 200 mm; AB = 940 mm; DB = 450 mm; PB = 600 mm; PC = 850 mm

Assignment

Due Date: 9 May 2017

Value: 400 of the 1000 marks for this course

I estimate that students who are fully competent in the course material will take 4-5 hours to complete this assignment. Student learning as they do the assignment may take between 20-25.

Question 1 (50 marks)

A car travelling on level ground at a constant 100 km/h drives off a 20 m high cliff. Treating the car as a particle and ignoring any air resistance, calculate the: (i) time taken for the car to reach the bottom of the cliff;

(ii) horizontal distance travelled from the cliff edge to the point of impact; and (iii) the velocity immediately before impact.

A comparison with similar accidents indicates that treating the car as a particle is not entirely accurate. Describe the motion that you expect if the engine is at the front of the vehicle and explain why you decided this was the case.

Question 2 (50 marks)

A 10 kg block is placed on an inclined surface as shown in the following diagram. Determine its kinetic energy and momentum at the instant it has traveled 250 mm from its initial placement. The static coefficient of friction between the block and inclined surface is 0.28 and the kinetic coefficient of friction is 0.22.

Question 3 (80 marks)

The end of cable D, as shown in the following figure, is pulled off the bottom of the drum with a horizontal velocity of 40 mm/s causing the cylinder to roll without slipping. Determine: (i) the angular velocity of the drum

(ii) the absolute velocity of centre A

(iii) the absolute velocity of point P

Question 4 (80 marks)

A slotted disc rotates clockwise as it decelerates uniformly from 120 rpm to rest in 3.5 seconds. At the same time object A is moving 0.5 m/s outward in the slot at a rate of 0.5 m / s2.

Determine the nett acceleration of A at the instant the disc attains a speed of 30 rpm. The position of A at this instant in time is depicted in the following diagram.

Question 5 (140 marks)

Rod AO in the ‘cross trainer’ mechanism shown below is rotating clockwise at a constant 45 rpm. At the position and instant shown determine the:

(i) absolute velocity of each point - A, B, C, and D

(ii) angular velocity of link AB and link BC

(iii) acceleration point A

(iv) acceleration point B and the angular acceleration of arm BC

OA = 200 mm; AB = 940 mm; DB = 450 mm; PB = 600 mm; PC = 850 mm

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