User:Inconspicuum/Physics (A Level)/Mechanics 2 Questions

Simple Harmonic Motion

 * 1) A 10N weight extends a spring by 5cm. Another 10N weight is added, and the spring extends another 5cm. What is the spring constant of the spring?
 * 2) The spring is taken into outer space, and is stretched 10cm with the two weights attached. What is the time period of its oscillation?
 * 3) What force is acting on the spring after 1 second? In what direction?
 * 4) A pendulum oscillates with a frequency of 0.5 Hz. What is the length of the pendulum?
 * 5) The following graph shows the displacement of a simple harmonic oscillator. Draw graphs of its velocity, momentum, acceleration and the force acting on it.
 * 1) A pendulum can only be modelled as a simple harmonic oscillator if the angle over which it oscillates is small. Why is this?

Energy in Simple Harmonic Motion

 * 1) A 10g mass causes a spring to extend 5cm. How much energy is stored by the spring?
 * 2) A 500g mass on a spring (k=100) is extended by 0.2m, and begins to oscillate in an otherwise empty universe. What is the maximum velocity which it reaches?
 * 3) Another 500g mass on another spring in another otherwise empty universe is extended by 0.5m, and begins to oscillate. If it reaches a maximum velocity of 15ms-1, what is the spring constant of the spring?
 * 4) Draw graphs of the kinetic and elastic energies of a mass on a spring (ignoring gravity).
 * 5) Use the trigonometric formulae for x and v to derive an equation for the total energy stored by an oscillating mass on a spring, ignoring gravity and air resistance, which is constant with respect to time.

Damping

 * 1) Draw a graph of displacement for a critically damped oscillation.
 * 2) How would you critically damp an oscillating pendulum?
 * 3) How would you damp an oscillating pendulum using only a weighted polystyrene block?
 * 4) What would the displacement graph look like for this oscillation, before and after damping began?
 * 5) The graph above is an exponentially damped oscillation. If the displacement of the undamped oscillation is given by sin &omega;t, what is an approximate equation for the damped oscillation, in terms of a constant k which describes the degree to which the oscillation is damped?

Conservation of Momentum

 * 1) A machine gun fires 300 5g bullets per. minute at 800ms-1. What force is exerted on the gun?
 * 2) 1 litre of water is pumped out of a tank in 5 seconds through a hose. If a 2N force is exerted on the tank, at what speed does the water leave the hose?
 * 3) If the hose were connected to the mains, what problems would there be with the above formula?
 * 4) The thrust of the first stage of a Saturn V rocket is 34 MN, using 131000kg of solid fuel in 168 seconds. At what velocity does the fuel leave the tank?
 * 5) Escape velocity from the Earth is 11km-1. What is the velocity of the rocket after the first stage is used up, if the total mass of the rocket is 3 x 106 kg? How does this compare to escape velocity?

Circular Motion

 * 1) A tennis ball of mass 10g is attached to the end of a 0.75m string and is swung in a circle around someone's head at a frequency of 1.5Hz. What is the tension in the string?
 * 2) A planet orbits a star in a circle. Its year is 100 Earth years, and the distance from the star to the planet is 70 Gm from the star. What is the mass of the star?
 * 3) A 2000kg car turns a corner, which is the arc of a circle, at 20kmh-1. The centripetal force due to friction is 1.5 times the weight of the car. What is the radius of the corner?
 * 4) Using the formulae for centripetal acceleration and gravitational field strength, and the definition of angular velocity, derive an equation linking the orbital period of a planet to the radius of its orbit.