M1 June 2017 Q5

EdexcelOld spec6 marksConnected Particles Forces & Newton's Laws

Figure 2: vertical rod PQ with a 0.5 kg particle at P on top and a 0.75 kg particle at Q below — Figure 2

A vertical light rod \(PQ\) has a particle of mass 0.5 kg attached to it at \(P\) and a particle of mass 0.75 kg attached to it at \(Q\), to form a system, as shown in Figure 2. The system is accelerated vertically upwards by a vertical force of magnitude 15 N applied to the particle at \(Q\). Find the thrust in the rod. (6)

Mark scheme

Scheme	Marks
\(T - 0.5g = 0.5a\)	M1 A1
\(15 - T - 0.75g = 0.75a\)	M1 A1
(OR: \(15 - 0.5g - 0.75g = 1.25a\))
(\(a = 2.2\) m s\(^{-2}\))
\(T = 6\) N	M1 A1
	(6 marks)

Notes

First M1 for an equation of motion for either \(P\) or \(Q\) with usual rules i.e. correct no. of terms, dimensionally correct but condone sign errors

First A1 for a correct equation (allow \(T\) replaced by \(-T\) and/or \(a\) replaced by \(-a\))

Second M1 for another equation of motion (for either \(P\) or \(Q\) or whole system) with usual rules as above

Second A1 for a correct equation (allow \(T\) consistently replaced by \(-T\) and/or \(a\) consistently replaced by \(-a\) )

Third M1 for solving two THREE term equations of motion for \(T\)

Third A1 for 6 (N). Must be positive but allow a change from −6 to 6, if they have consistently used \(-T\) instead of \(T\).