Moments

A footbridge across a stream is constructed by placing a tree trunk AB of length 8 m and mass 90 kg on to supports at A and B so that the tree trunk is horizontal
A woman of mass 60 kg stands on the trunk at C The magnitude of the reaction at A is twice the magnitude of the reaction at B. By modelling the tree trunk as a uniform rod and the woman as a particle calculate (a) the magnitude of the reaction at A and the magnitude of the reaction at B (b) the distance AC Describe the principal difference between your model and the real-life situation. How could your model be improved, using further information if necessary?

9 A uniform rod AB has length 6m and mass 4 kg. It is resting in equilibrium in a horizontal position on supports at points X and Y where AX=2m and AY = 4.5m. A particle of mass Mkg is placed at point C where AC = 5m. Given that the rod is on the point of tilting about Y, calculate the value of M

Reply 1

mqb2766

Original post by Martha Jones

A footbridge across a stream is constructed by placing a tree trunk AB of length 8 m and mass 90 kg on to supports at A and B so that the tree trunk is horizontal
A woman of mass 60 kg stands on the trunk at C The magnitude of the reaction at A is twice the magnitude of the reaction at B. By modelling the tree trunk as a uniform rod and the woman as a particle calculate (a) the magnitude of the reaction at A and the magnitude of the reaction at B (b) the distance AC Describe the principal difference between your model and the real-life situation. How could your model be improved, using further information if necessary?
9 A uniform rod AB has length 6m and mass 4 kg. It is resting in equilibrium in a horizontal position on supports at points X and Y where AX=2m and AY = 4.5m. A particle of mass Mkg is placed at point C where AC = 5m. Given that the rod is on the point of tilting about Y, calculate the value of M

What have you tried/what are you stuck with?

Reply 2

sam_6

Original post by Martha Jones

A footbridge across a stream is constructed by placing a tree trunk AB of length 8 m and mass 90 kg on to supports at A and B so that the tree trunk is horizontal
A woman of mass 60 kg stands on the trunk at C The magnitude of the reaction at A is twice the magnitude of the reaction at B. By modelling the tree trunk as a uniform rod and the woman as a particle calculate (a) the magnitude of the reaction at A and the magnitude of the reaction at B (b) the distance AC Describe the principal difference between your model and the real-life situation. How could your model be improved, using further information if necessary?
9 A uniform rod AB has length 6m and mass 4 kg. It is resting in equilibrium in a horizontal position on supports at points X and Y where AX=2m and AY = 4.5m. A particle of mass Mkg is placed at point C where AC = 5m. Given that the rod is on the point of tilting about Y, calculate the value of M

I would first start by drawing out a force diagram for the question. The trunk is uniform so the mass of 90kg will act downwards in the centre of the trunk (at 4metres). Label the magnitude at A as 2R and B as R.

a) to calculate the magnitude at A and B resolve forces upwards. The resultant force will equal 0 as the plank is in equilibrium. Make sure to include gravity as 'g' for the two downwards forces (the weights).