assignment

KNJ1023 Dynamics Prepared by: ASA

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Guideline:

Report should be written in hand writing

Deadline: Report has to be submitted on or before 17 April 2014

Question 1

A lorry K travels around the roundabout that has a radius of 50 m, as shown in Figure 1.

If the lorry increases its speed at a constant rate of 1.4 m/s2 starting from rest,

determine the time needed for the lorry to reach an acceleration of 1.6 m/s2.

Figure 1

FACULTY OF ENGINEERING

Department of Mechanical and Manufacturing Engineering

Semester 2 2013/2014

Assignment 1/2


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QUESTION 2

The position of a cyclist traveling along a straight road is described by the graph below

(Figure 2).

i. Draw the v – t graph that describes the motion in 20 s.

ii. Draw the a – t graph that describes the motion in 20 s.

Figure 2

Question 3

Wastewater from quarry operation released from a pipe as shown in Figure 3. The

water flow out from a pipe with a horizontal velocity of 10 m/s. Height of the pipe is 5 m

from the ground. Determine the time needed for the water to touch the ground and

range of L where the water touches the ground.


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Question 4

A 2 kg collar slide on a surface for which the coefficient of kinetic friction is k = 0.1. The

collar as shown in Figure 4 is attached to a spring having a stiffness k = 3 N/ m and

unstretched length of 0.4 m. If the collar is released from rest at A, calculate its

acceleration when the collar at C.

Figure 3

Figure 4


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QUESTION 5

The 800-kg car B is connected to the 350-kg car A by a spring coupling (Figure 5).

Given that there is some friction between the wheels of car B (take μkB = 0.4), while the

wheels of car A is free to roll (no friction);

i. Draw the free-body diagram of both cars.

ii. Determine the normal and frictional force developed at the wheels of car B.

iii. Determine the acceleration at which both cars (B & A) move.

iv. Determine the tension in the spring and its elongated (stretched) length.

v. Determine the acceleration at which both cars (A & B) move if the wheels of both

cars are free to rolls (no friction).

Figure 5

QUESTION 6

A 1500-kg car (Figure 6) moves along a circular track of radius 80 m, and its speed for a

short period of time 0 < t < 3 s is v = 0.9(t + t2) m/s, where t is in seconds. Determine;

i. The magnitude of the car’s acceleration when t = 3s .

ii. The distance the car travelled in t = 3s.


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iii. The minimum coefficient of static friction between the tires and the rod surface so

that the car does not slide when t = 5 s.

Figure 6

QUESTION 7

The 0.65-kg smooth can (Figure 7) is guided along the circular path using the arm OA.

At the instant shown ( ), the arms has an angular velocity and an

angular acceleration . Assuming that motion occurs in the vertical plane ;

i. Draw the free-body diagram of the can.

ii. Determine the r and components of the acceleration.

iii. Determine the force that arm OA exerts on the can.

iv. Draw the free-body diagram of the can, assuming that motion occurs in the

horizontal plane.


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Figure 7

Question 8

Figure 8 shows a man pushes on the 30 kg of hollow concrete structure from rest with a

force of F = 100 N. Determine the power supplied by the man when t = 5 s. The

coefficient of kinetic friction between the floor and the concrete structure is k = 0.2.

Figure 8


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QUESTION 9

In the following figure (Figure 9), both block J (30-kg) & K (20-kg) are initially at rest.

The coefficient of kinetic friction between both block J & K and the inclined plane is μk =

0.20.

Figure 9

a) Draw the free body diagrams (FBD) showing all the relevant forces acting on

block J and K; including the tension in the cable, T.

b) Using the equations of motion, determine the normal ( & ) and frictional (

& ) forces that act on block J and K.

c) Using kinematic equations for dependent motion of two particles, derive an

equation that relates the velocity of block J & K.

d) Using the principle of linear impulse and momentum, determine the velocity

of blocks J & K and also the tension in the cable, T when .

e) From your answer in (c), write an equation that relates the acceleration of block J

& K.

-End of questions-

assignment

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