HSC Physics Harder Circular Motion

A sheet of harder questions on circular motion follows.

1. A railroad car is moving around a horizontal circular track. On which rail, the inner or the outer, does a greater force act on the wheels of the car?
2. A railroad car is moving around a horizontal circular track of radius r with a speed v. The distance between the rails is d. If the height of the centre of gavity of the car above the rails is h, show that the ratio of the normal reaction reaction force exerted by the outer rail to the inner rail is (dgr + 2hv²)/(dgr - 2hv²).
3. A thin ring of radius R and mass M rotates at an angular speed ⍵. Find the tension in the ring. (a) Why is the tension in the ring not zero? (b) Show that the tension in the ring is M R ⍵²/(2𝜋).

HSC Physics Harder Projectile Motion

A sheet of harder questions on projectile motion is given below.

1. A particle is projected from a vertical height of 120.0 m at 30.0 m s^-1. Find the angles of projection to the horizontal if the horizontal range of the projectile is 100.0 m. Neglect air drag.
2. A stone is thrown at a speed U at 45° to the horizontal from a cliff of height h above sea level. The maximum height of the stone is 98.0 m and the horizontal displacement of the sone when it strikes the sea is 98.0 m. Find U and h. Take g = 9.8 m s^-2 and neglect air drag. (22.69 m s^-1, 84.87 m)