A uniform plank AB has mass 40 kg and length 4 m. It is supported in a horizontal position by two smooth pivots, one at the end A, the other at the point C of the plank where AC = 3 m, as shown in Fig. 1. A man of mass 80 kg stands on the plank which remains in equilibrium. The magnitudes of the reactions at the two pivots are each equal to R newtons. By modelling the plank as a rod and the man as a particle, find (a) the value of R, (b) the distance of the man from A.

A-Level Edexcel Maths Mechanics Newtons Second Law: A uniform plank AB has mass 40 k

A uniform plank AB has mass 40 kg and length 4 m - Edexcel - A-Level Maths Mechanics - Question 1 - 2003 - Paper 1

Question 1

A uniform plank AB has mass 40 kg and length 4 m. It is supported in a horizontal position by two smooth pivots, one at the end A, the other at the point C of the pl... show full transcript

Worked Solution & Example Answer:A uniform plank AB has mass 40 kg and length 4 m - Edexcel - A-Level Maths Mechanics - Question 1 - 2003 - Paper 1

Step 1

(a) the value of R

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Answer

To find the value of R, we start by applying the conditions for equilibrium.

Given that the total upward force must equal the total downward force, we have:

$ext{Total upward force} = R + R = 2R$ $ext{Total downward force} = 80g + 40g$

In this scenario, the weight of the man is contributed by his mass (80 kg) and the mass of the plank (40 kg). Therefore:

$2R = 80g + 40g$

Substituting the value of gravitational acceleration ( $g = 9.81 ext{ m/s}^2$ ), we calculate the values:

o $2R = 80 imes 9.81 + 40 imes 9.81$

o $2R = 1184.2 ext{ N}$

Finally, we solve for R:

$R = 592.1 ext{ N}$

Step 2

(b) the distance of the man from A

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Answer

To find the distance of the man from point A, we use the moments about point A.

The total clockwise moments are equal to the total counter-clockwise moments. The man exerts a moment about A while the plank also has its own.

The moment caused by the man is given by:

$ext{Moment}_{ ext{man}} = 80g imes x$

Where $x$ is the distance from A. The plank's weight creates a moment about A as follows:

$ext{Moment}_{ ext{plank}} = 40g imes 2$

Setting the total moments equal:

$80g imes x = 40g imes 2$

Now simplistically solve for x:

$x = \frac{40g imes 2}{80g} = 1.25 ext{ m}$

Thus, the distance of the man from A is 1.25 m.

A uniform plank AB has mass 40 kg and length 4 m - Edexcel - A-Level Maths Mechanics - Question 1 - 2003 - Paper 1

Worked Solution & Example Answer:A uniform plank AB has mass 40 kg and length 4 m - Edexcel - A-Level Maths Mechanics - Question 1 - 2003 - Paper 1

(a) the value of R

(b) the distance of the man from A

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