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jalex
jalex
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In the context of statics, you can treat multiple objects as one if you are not interested in any internal details. For example when analyzing a bridge, all the parts of the bridge can be treated as one body if only the support forces are needed.

In the context of dynamics, then you cannot treat multiple objects as one, unless they are kinematically linked to move together. Bodies that have different degrees of freedom, cannot be clumped together.

This particular problem is a quasi-static problem (slow moving painter) and canbut because the hinge between the ladders cannot transmit torque special care must be viewed as a statics problem at any time frametaken. So you can combine allThe torque to balance the parts togetherladders comes from the ground friction and so if you treat it as single body, but you have to ignoremust assume the pin can resist rotation, and convert the measured torque on the pin into an equivalent friction force.

It would be much simpler, to treat this with each body on their own (FBD diagrams), with each having their own balance equations. Two bodies, and three equations per body = 6 equations. Count your unknown forces betweenand find they are 6 also. Two per contact, and 2 at the two ladderspin.

In the context of statics, you can treat multiple objects as one if you are not interested in any internal details. For example when analyzing a bridge, all the parts of the bridge can be treated as one body if only the support forces are needed.

In the context of dynamics, then you cannot treat multiple objects as one, unless they are kinematically linked to move together. Bodies that have different degrees of freedom, cannot be clumped together.

This particular problem is a quasi-static problem (slow moving painter) and can be viewed as a statics problem at any time frame. So you can combine all the parts together, but you have to ignore the pin forces between the two ladders.

In the context of statics, you can treat multiple objects as one if you are not interested in any internal details. For example when analyzing a bridge, all the parts of the bridge can be treated as one body if only the support forces are needed.

In the context of dynamics, then you cannot treat multiple objects as one, unless they are kinematically linked to move together. Bodies that have different degrees of freedom, cannot be clumped together.

This particular problem is a quasi-static problem (slow moving painter) but because the hinge between the ladders cannot transmit torque special care must be taken. The torque to balance the ladders comes from the ground friction and so if you treat it as single body, you must assume the pin can resist rotation, and convert the measured torque on the pin into an equivalent friction force.

It would be much simpler, to treat this with each body on their own (FBD diagrams), with each having their own balance equations. Two bodies, and three equations per body = 6 equations. Count your unknown forces and find they are 6 also. Two per contact, and 2 at the pin.

Source Link
jalex
jalex
  • 3.3k
  • 1
  • 5
  • 19

In the context of statics, you can treat multiple objects as one if you are not interested in any internal details. For example when analyzing a bridge, all the parts of the bridge can be treated as one body if only the support forces are needed.

In the context of dynamics, then you cannot treat multiple objects as one, unless they are kinematically linked to move together. Bodies that have different degrees of freedom, cannot be clumped together.

This particular problem is a quasi-static problem (slow moving painter) and can be viewed as a statics problem at any time frame. So you can combine all the parts together, but you have to ignore the pin forces between the two ladders.