School of Mechanical and Electrical Engineering, Faculty of Health, Engineering and Sciences, MEC2401 Dynamics I, S2, 2014, Assignment 2

Answer all questions (200/1000) Due Date 27th October 2014

Assignment must be submitted electronically and student should follow the instructions given in the file “instructions for assignment preparation” which is posted on the course study desk Take gravitational acceleration g = 9.81 m/s2

Q1. (Marks 30/200)

The free rolling ramp shown in Figure Q1, a has mass of 90 kg . A crate whose mass is 60 kg slides from rest at A 6m down to the ramp to B.

I. Determine the ramps speed when the crate reaches B (Assume that the ramp surface and the floor are smooth) if ?=350 (10 Marks)

II. Determine the distance the ramp travels when the crate reaches B if ?=350 (Assume that the ramp surface and the floor are smooth) (10 Marks)

III. Describe the motion of rolling ramp, If the sliding friction coefficient of the ramp surface and the crate is 0.58 and the inclination angle ?=250 (10 Marks)

Figure Q1

Q2. (Marks 50/200)

At the instant shown in the Figure Q2, link AB has an angular velocity ?AB = 6 rad/s. angular acceleration aAB = 2 rad/s2. Each link is considered as a uniform slender bar each with a mass of 1.5 kg/m,

I. Determine the angular velocity and angular acceleration of link BC and CD (20 Marks)

II. Determine the kinetic energy of each link (AB, BC and CD) (15 Marks)

III. Determine the horizontal and vertical components of acceleration at point C (15 Marks)

Q3. (Marks 40/200)

Figure Q3 shows a 10Mg front-end-loader used to move Ore in the loader bucket. The centres of mass (CM) for the front-end-loader and the Ore load at G and GL respectively.

I. Determine the reactions exerted by the ground on the pairs of wheels at A and B, if the front-end-loader is moving forward at a constant acceleration of 1.6 m/s2 from the rest. The Ore Load is 2.5Mg and the CM

(GL) is at height h = 3.5 m and x = 2.0 m (from the centre of front wheel A). (20 Marks)

II. The front-end-loader with a 1 Mg Ore Load CM (GL) at h = 2.85 m and x= 2.6 m is moving forward at a constant velocity of 40 km/hr. Can the front-end-loader completely come to a rest safely without tipping over, if the operator suddenly applied brakes? Assume that all wheels are locked when the brakes are applied and the coefficient of static friction between the wheels and the ground is 0.55. (20 Marks)

Figure Q3

Q4. (Marks 40/200)

Figure Q4 shows a uniform disk attached to a shaft at A (in vertical plane). Disk has a mass (M) 15 kg and G is the centre of mass. A constant torque of T = 50 N m is exerted on the disk by the shaft at A and the disk start rotating about the shaft’s horizontal axis (perpendicular to the sheet). Initially time t = 0 s and ? = 00.

I. Derive an expression for the resulting angular acceleration of the disk and calculate the angular acceleration at the instant ? = 450. (15 Marks)

II. Calculate the rotational speed (rpm) of the disk around A, kinetic energy of the disk and the work done by the torque T after ? = 450. (15 Marks)

III. Calculate the radial force acting on the shaft by the disk and its direction with respect to Y axis, when at ? = 450. Illustrate it on a free-body-diagram (Marks 10)

Figure Q4

Q5. (Marks 40/200)

Figure Q5 shows a collision of a high speed locomotive engine and an oil tanker at an unprotected railway crossing. The locomotive A has mass MA and was travelling in constant velocity of 120 km/hr and the Tanker B has mass MB and was travelling in constant velocity of 80 km/hr. MA = 5 Mg and MB = 1.8 Mg

I. Calculate velocities of the locomotive and the tanker after the collision if the locomotive and the tanker become entangled and move off together after the collision. (10 Marks)

II. Calculate velocities of the locomotive and the tanker after the collision in terms of e (0 e 1) which the coefficient of restitution between the locomotive and the tanker. (20 Marks)

III. Calculate the possible energy loss for Case (i) and Case (II) for two values of e; 0.2, and 0.8. Comment on the severity of collision depending on your calculated values. (10 Marks)

List all the assumptions clearly for each case.

Figure Q5

Answer all questions (200/1000) Due Date 27th October 2014

Assignment must be submitted electronically and student should follow the instructions given in the file “instructions for assignment preparation” which is posted on the course study desk Take gravitational acceleration g = 9.81 m/s2

Q1. (Marks 30/200)

The free rolling ramp shown in Figure Q1, a has mass of 90 kg . A crate whose mass is 60 kg slides from rest at A 6m down to the ramp to B.

I. Determine the ramps speed when the crate reaches B (Assume that the ramp surface and the floor are smooth) if ?=350 (10 Marks)

II. Determine the distance the ramp travels when the crate reaches B if ?=350 (Assume that the ramp surface and the floor are smooth) (10 Marks)

III. Describe the motion of rolling ramp, If the sliding friction coefficient of the ramp surface and the crate is 0.58 and the inclination angle ?=250 (10 Marks)

Figure Q1

Q2. (Marks 50/200)

At the instant shown in the Figure Q2, link AB has an angular velocity ?AB = 6 rad/s. angular acceleration aAB = 2 rad/s2. Each link is considered as a uniform slender bar each with a mass of 1.5 kg/m,

I. Determine the angular velocity and angular acceleration of link BC and CD (20 Marks)

II. Determine the kinetic energy of each link (AB, BC and CD) (15 Marks)

III. Determine the horizontal and vertical components of acceleration at point C (15 Marks)

Q3. (Marks 40/200)

Figure Q3 shows a 10Mg front-end-loader used to move Ore in the loader bucket. The centres of mass (CM) for the front-end-loader and the Ore load at G and GL respectively.

I. Determine the reactions exerted by the ground on the pairs of wheels at A and B, if the front-end-loader is moving forward at a constant acceleration of 1.6 m/s2 from the rest. The Ore Load is 2.5Mg and the CM

(GL) is at height h = 3.5 m and x = 2.0 m (from the centre of front wheel A). (20 Marks)

II. The front-end-loader with a 1 Mg Ore Load CM (GL) at h = 2.85 m and x= 2.6 m is moving forward at a constant velocity of 40 km/hr. Can the front-end-loader completely come to a rest safely without tipping over, if the operator suddenly applied brakes? Assume that all wheels are locked when the brakes are applied and the coefficient of static friction between the wheels and the ground is 0.55. (20 Marks)

Figure Q3

Q4. (Marks 40/200)

Figure Q4 shows a uniform disk attached to a shaft at A (in vertical plane). Disk has a mass (M) 15 kg and G is the centre of mass. A constant torque of T = 50 N m is exerted on the disk by the shaft at A and the disk start rotating about the shaft’s horizontal axis (perpendicular to the sheet). Initially time t = 0 s and ? = 00.

I. Derive an expression for the resulting angular acceleration of the disk and calculate the angular acceleration at the instant ? = 450. (15 Marks)

II. Calculate the rotational speed (rpm) of the disk around A, kinetic energy of the disk and the work done by the torque T after ? = 450. (15 Marks)

III. Calculate the radial force acting on the shaft by the disk and its direction with respect to Y axis, when at ? = 450. Illustrate it on a free-body-diagram (Marks 10)

Figure Q4

Q5. (Marks 40/200)

Figure Q5 shows a collision of a high speed locomotive engine and an oil tanker at an unprotected railway crossing. The locomotive A has mass MA and was travelling in constant velocity of 120 km/hr and the Tanker B has mass MB and was travelling in constant velocity of 80 km/hr. MA = 5 Mg and MB = 1.8 Mg

I. Calculate velocities of the locomotive and the tanker after the collision if the locomotive and the tanker become entangled and move off together after the collision. (10 Marks)

II. Calculate velocities of the locomotive and the tanker after the collision in terms of e (0 e 1) which the coefficient of restitution between the locomotive and the tanker. (20 Marks)

III. Calculate the possible energy loss for Case (i) and Case (II) for two values of e; 0.2, and 0.8. Comment on the severity of collision depending on your calculated values. (10 Marks)

List all the assumptions clearly for each case.

Figure Q5

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