EM220 MEC420 –Dynamics Faculty of Mechanical Engineering Universiti Teknologi MARA

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Tutorial Set No. 2: Kinematics of Particles

1-1 Car A moves with the initial velocity of 15 m/s at an acceleration given by 2.5t m/s2 where t is time in seconds, while car B which is 100 m ahead of car A starts moving from rest at a constant acceleration of 10 m/s2. If both cars start at the same time and move in the same direction, determine whether car A will eventually overtake car B. If yes, at what position and time?

Figure T 1.1

1-2 An object is moving in a straight path according to v2 = k/x where v is the velocity in m/s, x is the distance traveled in m, and k is a constant. Knowing that at time t = 0 s, the velocity is 2 m/s, and its position is 2 m, determine the velocity of the object at t = 3 s.

Figure T 1.2

1-3 In certain experiment of a newly-designed parachute, the acceleration of the falling parachutist is given by a = -0.4v1.5. Show that the displacement x, velocity v, and time t

of the parachutist can be related by equation x = t vvo where vo is the initial velocity

and xo = 0 m. What was the falling distance of the parachutist in 3 s if his initially velocity was 25 m/s?

Figure T 1.3

1-4 Consider a mass-pulley system as shown in the figure. Knowing that block B moves downward at a speed of 10 m/s and is increasing at 5 m/s2, determine (a) the velocity and acceleration at which block A is raised, (b) the displacement of block A after 2 s, and (c) the velocity of block A relative to block B.

Figure T 1.4

1-5 For the mass-pulley system as shown, determine the velocity at which block B is raised if the roller A moves rightward with a speed of 10 m/s at the instant when x = 4 m. Given the height h = 12 m.

A

B

Figure T 1.5

1-6 A missile is fired horizontally with an initial velocity v0 from point A located 3 m above

the ground. If the missile just passes over the wall at B and hits the target at C, determine (a) the value of v0 and (b) the distance d.

Figure T 1.6

1-7 Rod AB rotates clockwise with a constant angular rate of 5 rad/s. A double collar C is

pin-connected together such that one collar slides over the straight rod AB and the other over the curved rod DE. If the curved shape is given by the equation r = (2.5 – cos

) m, where is in radians, determine the magnitude of the velocity and acceleration of

the double collar when = 30o.

Figure T 1.7

1-8 Pin P is attached to the rim of the rotating disk and slides into the slotted bar

OA in the figure. When = 45 0 the angular velocity of OA is = 0.5 rad/s. For

A

B

E

C

D

r

A

B

C

12 m d

3 m

1.8 m

A

B

C

h

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x

this position determine and R (the angular velocity of the disk and the

velocity of P relative to the arm OA).

O

A

B

P

200

R

80

Dimensions in mm

O

A

B

P

200

R

80

Dimensions in mm

Figure T 1.8 1-9 A package which is initially at rest at A on an industrial conveyor belt moves with a

constant acceleration of 6 m/s2. Determine the total acceleration of the package when it arrives at position B.

Figure T 1.9

1-10 For the instant represented in the figure, the racing car A is rounding the circular curve

at a speed of 110 km/h and is accelerating at 3 m/s2 after coming off a pit stop, while car B is moving at 130 km/h but is slowing down at the rate of 2 m/s2. Determine the velocity and acceleration of car B relative to car A.

Figure T 1.10

150 m

A

B

A

B

2.1

m

s

4 m

t

n