A-Level Edexcel Maths Mechanics Forces: A uniform plank AB has weight 12

A uniform plank AB has weight 120 N and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1

Question 2

A uniform plank AB has weight 120 N and length 3 m. The plank rests horizontally in equilibrium on two smooth supports C and D, where AC = 1 m and CD = x m, as shown... show full transcript

Worked Solution & Example Answer:A uniform plank AB has weight 120 N and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1

Step 1

show that $x = 0.75$

96%

114 rated

Answer

To determine the value of $x$ , we need to consider the moments about point C. The moment due to the reaction at D is given by:

$M(C) = R_D imes x = 80 imes x$

The moment due to the weight of the plank (acting at its center, which is at 1.5 m from C) is given by:

$M(A) = W imes 0.5 = 120 imes 0.5$

Setting these moments equal for equilibrium, we have:

$80x = 120 imes 0.5$

Solving for $x$ gives:

$x = \frac{120 \times 0.5}{80} = 0.75.$

Thus, we have confirmed that $x = 0.75$ .

Step 2

the weight of the rock

99%

104 rated

Answer

When a rock is placed at point B and the plank is on the verge of tilting about D, we consider the moments around D.

Using the equilibrium of moments:

$M(D) = 120 imes 0.25 - W \times 1.25 = 0,$

giving us:

$120 \times 0.25 = W \times 1.25.$

Thus,

$W = \frac{120 \times 0.25}{1.25} = 24 \text{ N}.$

Step 3

the magnitude of the reaction of the support on the plank at D

96%

101 rated

Answer

The total weight acting on the plank includes both the weight of the plank and the weight of the rock:

$X = W + 120 = 24 + 120 = 144 \text{ N}.$

Step 4

State how you have used the model of the rock as a particle

98%

120 rated

Answer

In this model, the rock is considered a particle, meaning its shape and rotational effects are neglected. This simplification allows us to concentrate solely on its weight acting at point B without considering its geometry or distribution of mass.

A uniform plank AB has weight 120 N and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1

Worked Solution & Example Answer:A uniform plank AB has weight 120 N and length 3 m - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1

show that $x = 0.75$

the weight of the rock

the magnitude of the reaction of the support on the plank at D

State how you have used the model of the rock as a particle

Join the A-Level students using SimpleStudy...