# 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) Solution Marks (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)

$v_v = 200 \sin 60 = 173\; \text {m/s} \\ \Delta y = v_0t+ \frac{1}{2}at^2 \\ 0 = 173(t)- 4.9 t^2$ (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)