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### MICHAELERRON

#### Cambridge International AS and A Level

 Name of student MICHAELERRON Date Adm. number Year/grade 1989 Stream Michaelerron Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 8 6 7 8 8 8 45
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/41/M/J/15/5, Topic: - A cyclist and her bicycle have a total mass of$84 \mathrm{~kg}$. She works at a constant rate of$P \mathrm{~W}$while moving on a straight road which is inclined to the horizontal at an angle$\theta$, where$\sin \theta=0.1$. When moving uphill, the cyclist's acceleration is$1.25 \mathrm{~m} \mathrm{~s}^{-2}$at an instant when her speed is$3 \mathrm{~m} \mathrm{~s}^{-1}$. When moving downhill, the cyclist's acceleration is$1.25 \mathrm{~m} \mathrm{~s}^{-2}$at an instant when her speed is$10 \mathrm{~m} \mathrm{~s}^{-1}$. The resistance to the cyclist's motion, whether the cyclist is moving uphill or downhill, is$R \mathrm{~N}$. Find the values of$P$and$R$.$$Question 2 Code: 9709/42/M/J/15/5, Topic: - A particle$P$starts from rest at a point$O$on a horizontal straight line.$P$moves along the line with constant acceleration and reaches a point$A$on the line with a speed of$30 \mathrm{~m} \mathrm{~s}^{-1}$. At the instant that$P$leaves$O$, a particle$Q$is projected vertically upwards from the point$A$with a speed of$20 \mathrm{~m} \mathrm{~s}^{-1}$. Subsequently$P$and$Q$collide at$A$. Find$\text{(i)}$the acceleration of$P$,$\text{(ii)}$the distance$O A$.$$Question 3 Code: 9709/43/M/J/15/5, Topic: - ![9709-43-M-J-15-5a.PNG] Four coplanar forces of magnitudes$4 \mathrm{~N}, 8 \mathrm{~N}, 12 \mathrm{~N}$and$16 \mathrm{~N}$act at a point. The directions in which the forces act are shown in Fig. 1.$\text{(i)}$Find the magnitude and direction of the resultant of the four forces.$$ ![9709-43-M-J-15-5b.PNG] The forces of magnitudes$4 \mathrm{~N}$and$16 \mathrm{~N}$exchange their directions and the forces of magnitudes$8 \mathrm{~N}$and$12 \mathrm{~N}$also exchange their directions (see Fig. 2).$\text{(ii)}$State the magnitude and direction of the resultant of the four forces in Fig.$2.$Question 4 Code: 9709/41/O/N/15/5, Topic: - A small bead$Q$can move freely along a smooth horizontal straight wire$A B$of length$3 \mathrm{~m}$. Three horizontal forces of magnitudes$F \mathrm{~N}, 10 \mathrm{~N}$and$20 \mathrm{~N}$act on the bead in the directions shown in the diagram. The magnitude of the resultant of the three forces is$R \mathrm{~N}$in the direction shown in the diagram.$\text{(i)}$Find the values of$F$and$R$.$\text{(ii)}$Initially the bead is at rest at$A$. It reaches$B$with a speed of$11.7 \mathrm{~m} \mathrm{~s}^{-1}$. Find the mass of the bead.$$Question 5 Code: 9709/42/O/N/15/5, Topic: - A smooth inclined plane of length$2.5 \mathrm{~m}$is fixed with one end on the horizontal floor and the other end at a height of$0.7 \mathrm{~m}$above the floor. Particles$P$and$Q$, of masses$0.5 \mathrm{~kg}$and$0.1 \mathrm{~kg}$respectively, are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the top of the plane. Particle$Q$is held at rest on the floor vertically below the pulley. The string is taut and$P$is at rest on the plane (see diagram).$Q$is released and starts to move vertically upwards towards the pulley and$P$moves down the plane.$\text{(i)}$Find the tension in the string and the magnitude of the acceleration of the particles before$Q$reaches the pulley.$$At the instant just before$Q$reaches the pulley the string breaks;$P$continues to move down the plane and reaches the floor with a speed of$2 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(ii)}$Find the length of the string.$$Question 6 Code: 9709/43/O/N/15/5, Topic: - A cyclist and his bicycle have a total mass of$90 \mathrm{~kg}$. The cyclist starts to move with speed$3 \mathrm{~ms}^{-1}$from the top of a straight hill, of length$500 \mathrm{~m}$, which is inclined at an angle of$\sin ^{-1} 0.05$to the horizontal. The cyclist moves with constant acceleration until he reaches the bottom of the hill with speed$5 \mathrm{~m} \mathrm{~s}^{-1}$. The cyclist generates$420 \mathrm{~W}$of power while moving down the hill. The resistance to the motion of the cyclist and his bicycle,$R \mathrm{~N}$, and the cyclist's speed,$v \mathrm{~m} \mathrm{~s}^{-1}$, both vary.$\text{(i)}$Show that$\displaystyle R=\frac{420}{v}+43.56\text{(ii)}$Find the cyclist's speed at the mid-point of the hill. Hence find the decrease in the value of$R$when the cyclist moves from the top of the hill to the mid-point of the hill, and when the cyclist moves from the mid-point of the hill to the bottom of the hill.$\$

Worked solutions: P1, P3 & P6 (S1)

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