PHYS*1080 Sample Quiz 6
- A dead fly of mass 1.5×10−3kg is tangled in a strand of spider's web. The fly's weight stretches the strand as shown. Calculate the magnitudes of the tensions T1 and T2 in the two branches of the strand. (5 marks)
Solution Marks 
(1.0) Diagram x:−T1cos50∘+T2sin70∘=0 (1.0) ∴ (0.5) y: \quad T_1 \sin 50^\circ - T_2 \cos 70^\circ - mg = 0 (1.0) \text{Substitute from}(A): \\ T_1 \bigg( \sin 50^\circ - \frac{\cos 50^\circ}{\sin 70^\circ} \cos 70^\circ \bigg) = mg (0.5) \therefore 0.532\;T_1 = 1.5 \times 10^{-3} \times 9.8 \\ \therefore T_1 = 2.8 \times 10^{-2}\; \text N (0.5) \text{Substituting back into}\; (A): \\ \quad T_2 = 0.684\times T_1 = 1.9 \times 10 ^{-2} \; \text N (0.5)
- A hammer with a 1.4\;\text{kg} head is used to drive a nail into a board. The hammer is moving at 5.0\; \text{m/s} when i strikes the nail, driving the nail 1.0 \; \text{cm} into the board. What is the average force the hammer exerts on the nail? (2 marks)
Solution Marks Kinetic energy of hammer head = Work done on nail. (1.0) 1/2 mv^2 = F_{av} \times distance \\ 1/2 1.4 \times 5.0^2 = F_{av} \times 0.01 \; \text m (0.5) \therefore \; F_{av} = 1.8 \times 10^3\; \text N (0.5)
- A cannon fires a ball with a muzzle velocity of 200\; \text{m/s} at an angle of 60.0^\circ above the horizontal. How far down range does the ball land? (Neglect air friction.) (3 marks)
Solution Marks v_v = 200 \sin 60 = 173\; \text {m/s} \\ \Delta y = v_0t+ \frac{1}{2}at^2 \\ 0 = 173(t)- 4.9 t^2 (0.5) t = 173/4.9 = 35.3 \; \text s (1.0) v_h = 200 \cos 60 = 100\; \text {m/s} (0.5) d = vt = 100 \times 35.3 = 3530 \; \text m (1.0)
