$\require{\cancel}$ $\require{\stix[upint]}$

### HENRYTAIGO

#### Cambridge International AS and A Level

 Name of student HENRYTAIGO Date Adm. number Year/grade HenryTaigo Stream HenryTaigo Subject Mechanics 2 (M2) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 8 7 8 8 8 9 48
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/51/M/J/15/5, Topic: - A particle$P$of mass$0.3 \mathrm{~kg}$is attached to one end of a light elastic string of natural length$0.9 \mathrm{~m}$and modulus of elasticity$18 \mathrm{~N}$. The other end of the string is attached to a fixed point$O$which is$3 \mathrm{~m}$above the ground.$\text{(i)}$Find the extension of the string when$P$is in the equilibrium position.$[2]P$is projected vertically downwards from the equilibrium position with initial speed$6 \mathrm{~m} \mathrm{~s}^{-1}.$At the instant when the tension in the string is$12 \mathrm{~N}$the string breaks.$P$continues to descend vertically.$\text{(ii)}~~\text{(a)}$Calculate the height of$P$above the ground at the instant when the string breaks.$[2]\text{(b)}$Find the speed of$P$immediately before it strikes the ground.$[4]$Question 2 Code: 9709/52/M/J/15/5, Topic: - A uniform solid cube with edges of length$0.4 \mathrm{~m}$rests in equilibrium on a rough plane inclined at an angle of$30^{\circ}$to the horizontal.$A B C D$is a cross-section through the centre of mass of the cube, with$A B$along a line of greatest slope.$B$lies below the level of$A$. One end of a light elastic string with modulus of elasticity$12 \mathrm{~N}$and natural length$0.4 \mathrm{~m}$is attached to$C$. The other end of the string is attached to a point below the level of$B$on the same line of greatest slope, such that the string makes an angle of$30^{\circ}$with the plane (see diagram). The cube is on the point of toppling. Find$\text{(i)}$the tension in the string,$[3]\text{(ii)}$the weight of the cube.$[4]$Question 3 Code: 9709/53/M/J/15/5, Topic: - A uniform triangular prism of weight$20 \mathrm{~N}$rests on a horizontal table.$A B C$is the cross-section through the centre of mass of the prism, where$B C=0.5 \mathrm{~m}, A B=0.4 \mathrm{~m}, A C=0.3 \mathrm{~m}$and angle$B A C=90^{\circ}$. The vertical plane$A B C$is perpendicular to the edge of the table. The point$D$on$A C$is at the edge of the table, and$A D=0.25 \mathrm{~m}$. One end of a light elastic string of natural length$0.6 \mathrm{~m}$and modulus of elasticity$48 \mathrm{~N}$is attached to$C$and a particle of mass$2.5 \mathrm{~kg}$is attached to the other end of the string. The particle is released from rest at$C$and falls vertically (see diagram).$\text{(i)}$Show that the tension in the string is$60 \mathrm{~N}$at the instant when the prism topples.$[3]\text{(ii)}$Calculate the speed of the particle at the instant when the prism topples.$[5]$Question 4 Code: 9709/51/O/N/15/5, Topic: - A particle$P$of mass$0.2 \mathrm{~kg}$is attached to one end of a light elastic string of natural length$0.75 \mathrm{~m}$and modulus of elasticity$21 \mathrm{~N}$. The other end of the string is attached to a fixed point$A$which is$0.8 \mathrm{~m}$vertically above a smooth horizontal surface.$P$rests in equilibrium on the surface.$\text{(i)}$Find the magnitude of the force exerted on$P$by the surface.$[2]P$is now projected horizontally along the surface with speed$3 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(ii)}$Calculate the extension of the string at the instant when$P$leaves the surface.$[3]\text{(iii)}$Hence find the speed of$P$at the instant when it leaves the surface.$[3]$Question 5 Code: 9709/52/O/N/15/5, Topic: - Question 6 Code: 9709/53/O/N/15/5, Topic: - A particle$P$of mass$0.5 \mathrm{~kg}$is projected vertically upwards from a point on a horizontal surface. A resisting force of magnitude$0.02 v^{2} \mathrm{~N}$acts on$P$, where$v \mathrm{~m} \mathrm{~s}^{-1}$is the upward velocity of$P$when it is a height of$x \mathrm{~m}$above the surface. The initial speed of$P$is$8 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(i)}$Show that, while$P$is moving upwards,$v \displaystyle\frac{\mathrm{d} v}{\mathrm{~d} x}=-10-0.04 v^{2}$.$[2]\text{(ii)}$Find the greatest height of$P$above the surface.$[3]\text{(iii)}$Find the speed of$P$immediately before it strikes the surface after descending.$[4]\$

Worked solutions: P1, P3 & P6 (S1)

If you need worked solutions for P1, P3 & P6 (S1), contact us @ [email protected] | +254 721 301 418.

1. Send us the link to these questions ( https://stemcie.com/view/107 ).
2. We will solve the questions and provide you with the step by step worked solutions.
3. We will then schedule a one to one online session to take you through the solutions (optional).