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## Worked example 4.4: Suspended block

Question: Consider the diagram. The mass of block is and the mass of block is . The coefficient of static friction between the two blocks is . The horizontal surface is frictionless. What minimum force must be exerted on block in order to prevent block from falling? Answer: Suppose that block exerts a rightward force on block . By Newton's third law, block exerts an equal and opposite force on block . Applying Newton's second law of motion to the rightward acceleration of block , we obtain where is the mass of block . The normal reaction at the interface between the two blocks is . Hence, the maximum frictional force that block can exert on block is . In order to prevent block from falling, this maximum frictional force (which acts upwards) must exceed the downward acting weight, , of the block. Hence, we require or Applying Newton's second law to the rightward acceleration of both blocks (remembering that the equal and opposite forces exerted between the blocks cancel one another out), we obtain where is the mass of block . It follows that Since , , and , we have    Next: Conservation of energy Up: Newton's laws of motion Previous: Worked example 4.3: Raising
Richard Fitzpatrick 2006-02-02