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Task 4: Matrices problem The following dynamic pulley system is released from rest.

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a₁

T₁

Instructions for the Further maths coursework.

4kg

7₂

7kg

a₂ + a₂

T₁

a₁

T₂

3kg

az-a

1.Draw a free body diagram for each particle within the system.

(2)

(2)

2.State four modelling assumptions you will use for this system.

3.Using Newtons Laws of motion, derive an equation of motion for each particle.

(4)

4.Using matrix algebra, setup the solution matrix in the form Ax=B.

5.Solve this matrix to find the variables of the pulley system, using an analytical method,

showing each step. Write each step in the equation builder in Microsoft Word.

(4)

6.Solve the same matrix using the available formulae in Microsoft Excel. (2)

(2)

7.Compare the two solutions; they should be identical.

8. Comment on the matrix method and its usefulness in mechanical problems like this

one. What are the advantages of building a matrix to model and solve modelling

(2)

20

Fig: 1