Course:PHYS350/Tutorial 0 2007W

http://www.nytimes.com/2007/09/04/science/04cat.html

1. An object A moving with velocity v collides with a stationary object B. After the collision, A is moving with velocity v/2 and B with velocity 3v/2. Find the ratio of the masses. If, instead of bouncing apart, the two bodies stuck together after the collision, with what velocity would they move?

2. The two components of a double star are observed to move in circles of radii $r_{1}$ and $r_{2}$. What is the ratio of their masse? (Hint: Write down their accelerations in terms of the angular velocity of rotation, ω.)

6. A body of mas 50kg is suspended by two light, inextensible cables of lengths 15m and 20m from rigid supports places 25m apart on the same level. Find the tensions in the cables. (Note that by convention 'light' means 'of negligible mass'. Take g=10ms^-2)

10. The first estimate of Newton's constant was made by astronomer Nevil Maskelyne in 1774 by measuring the angle between the directions of the apparent plumb-line vertical on opposite sides of the Scottish mountain Schiehallion (height 1081m, chosen for its regular conical shape). Find a rough estimate of the angle through which a plumb line is deviated by the gravitational attraction of the mountain, by modelling the mountain as sphere of radius 500m and density $2.3\times 10^{3}$ kg m^-3, and assuming that its gravitational effect is the same as though the total mass were concentrated at its centre. (This latter assumption will be justified, for a spherical object, in Chapter 6).