M3 January 2010 Q4

EdexcelOld spec10 marksHooke's Law

Figure 3: particle P hanging on a string from O, pulled aside by a horizontal force of 30 N — Figure 3

A particle \(P\) of weight 40 N is attached to one end of a light elastic string of natural length 0.5 m. The other end of the string is attached to a fixed point \(O\). A horizontal force of magnitude 30 N is applied to \(P\), as shown in Figure 3. The particle \(P\) is in equilibrium and the elastic energy stored in the string is 10 J.

Calculate the length \(OP\). (10)

Force diagram: tension T along PO at angle theta to the vertical, 30 N horizontal and 40 N down at P — Mark scheme

Scheme	Marks
\(\uparrow \quad T\cos\theta = 40\)	M1 A1
\(\rightarrow \quad T\sin\theta = 30\)	A1
leading to \(\quad T = 50\)	M1 A1
\(E = \dfrac{\lambda x^2}{2a} = 10\)	B1
HL \(\quad T = \dfrac{\lambda x}{a} = 50\)	M1
leading to \(\quad x = 0.4\)	M1 A1
\(OP = 0.5 + 0.4 = 0.9\ (\text{m})\)	A1ft
	(10)
	(10 marks)

Notes