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M1 help needed

Please can someone explain question 4c please:
QP: https://docs.google.com/viewer?url=http://www.edexcel.com/migrationdocuments/QP%2520GCE%2520Curriculum%25202000/Maths/09_M1_January_2005.doc
MS: https://docs.google.com/viewer?url=http://www.edexcel.com/migrationdocuments/QP%2520GCE%2520Curriculum%25202000/Maths/M1_January_2005_mark_scheme.doc

I understand that they've found two values for the friction- one where it's equal to the weight component parallel to the plane, and the other where they've used F=muR, but I don't understand how saying one of the values is less than the other shows it's in equilibrium..?
Original post by bobbricks


I understand that they've found two values for the friction- one where it's equal to the weight component parallel to the plane, and the other where they've used F=muR, but I don't understand how saying one of the values is less than the other shows it's in equilibrium..?


The frictional force worked out using the component of the weight parallel to the plane is the actual frictional force.

F=muR gives you the maximum possible frictional force. The force when you have limiting equilibrium (i.e. on the point of slipping).

Since the former is less than the latter, the particle doesn't move.

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