PHYS*1080 Sample Quiz 6

  1. A dead fly of mass \(1.5 \times 10^{-3}\; \text{kg}\) is tangled in a strand of spider's web. The fly's weight stretches the strand as shown. Calculate the magnitudes of the tensions \(T_1\) and \(T_2\) in the two branches of the strand. (5 marks)
    diagram of a fly in a web
    Solution Marks
    diagram of tension on web with fly in it (1.0) Diagram
    \(x: \quad -T_1 \cos 50^\circ + T_2 \sin 70^\circ = 0\) (1.0)
    \(\quad \therefore T_2 = T_1 \frac{\cos 50^\circ}{\sin 70^\circ} \quad (A)\) (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)
    \(\text{Substituting back into}\; (A): \\ \quad T_2 = 0.684, T_1 = 1.9 \times 10 ^{-2} \; \text N\) (0.5)
     
     
  2. 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)

     
  3. 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)