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 ωt, 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.