Q1.

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 θ=35⁰

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

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 θ=25⁰

Q2.

At the instant shown in the Figure Q2, link AB has an angular velocity ω_AB = 6 rad/s. angular acceleration α_AB = 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
II. Determine the kinetic energy of each link (AB, BC and CD)
III. Determine the horizontal and vertical components of acceleration at point C

Q3.

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).

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.

Q4.

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 θ = 0⁰.

I. Derive an expression for the resulting angular acceleration of the disk and calculate the angular acceleration at the instant θ = 45⁰.

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 θ = 45⁰.

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

Q5.

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 M_A and was travelling in constant velocity of 120 km/hr and the Tanker B has mass M_B and was travelling in constant velocity of 80 km/hr. M_A = 5 Mg and M_B = 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.

II. Calculate velocities of the locomotive and the tanker after the collision in terms of e (0

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.

List all the assumptions clearly for each case.