Particle A has a mass of 0.6 kg and is confined to move without friction along a smooth horizontal
slot due to the rotation of the arm OP as presented in Figure Q1. The arm OP is rotating with a
constant angular velocity w = 2.4 rad/s. Assume the particle contacts only one side of the slot at
any instant. At the instant shown (O = 32°) in Figure Q1, determine:
1. The force of the arm OP on particle A.
2. The normal force of the slot on particle A.
Equation of motion about fixed axis
OB = 0.707507042m
(aG)n = w2r=2.42 X 0. 7075 = 4.07524rad/s2
= 2.4 rad/s
The 35-kg reel is mounted on the 24-kg cart as shown in Figure Q2. A cable wrapped around the
inner hub of the reel is subjected to a force of P = 48 N. The radius of gyration of the reel about its
mass center o is ko = 260 mm. Other parameters are given in Figure Q2. Neglect the size of the
1. Draw the Free Body Diagrams of the reel and the cart.
2. Determine the velocity of the cart at time t = 5s
3. Determine the angular velocity of the reel at time t = 5s.
P = 48 N
The drum has a mass of 58 kg and a radius of gyration about the pin at o of ko = 0.25m.
Starting from rest, the suspended 18-kg block B is allowed to fall 3.2 m without applying the brake
1. Determine the speed of the block B at this instant (see Figure Q3).
2. A force P is applied at the brake handle D as shown in Figure Q3 to stop the block B after it
descends another 3.2 m. The coefficient of kinetic friction at the brake pad C is uk = 0.5 and
neglect the thickness of the handle.
- Draw the Free Body Diagrams of the drum and the brake ACD.
- Determine the force P
At the instant shown in the Figure Q4, link AB has an angular velocity BAB = 3.5 rad/s and angular
acceleration aAB = 2.2 rad/s2. Each link is considered as a uniform slender bar with a mass of 2.0
Determine the angular velocity and angular acceleration of link BC and link CD
2. Determine the kinetic energy of each link (AB, BC and CD)
3. Determine the horizontal and vertical components of acceleration at point C
2.2 rad/s 2
Figure Q5 shows a collision of a high speed locomotive engine and an oil tanker at a unprotected
railway crossing. The locomotive A has mass MA = 4.' 7 Mg and was travelling in constant
velocity of 100 km/h and the Tanker B has mass MB = 1.4 Mg and was travelling in constant
velocity of 80 km/h.
1. 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..
2. Calculate velocities of the locomotive and the tanker after the collision in terms of e (0
which is the coefficient of restitution between the locomotive and the tanker.
3. Calculate the possible energy losses for Case (1) and Case (2) for the value of e = 0.8. Comment
on the severity of collision depending on your calculated values.
List all the assumptions clearly for each case.
V (loco) = 100 km/h
V (Tanker) 80 km/h
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