Questions & Answers (Hints) - 3

Question   (11 marks)

(a)  Figure given below shows the envelope of the vibrations of a stretched string that is emitting a note at its fundamental frequency.

      (i)  Draw on the figure given below; the shape of the envelope of the vibrations when the string is emitting a note at three times its fundamental frequency.   (1 mark)

     (ii)  Explain briefly how a stationary wave, such as that shown in the figure above, is produced.   (2 marks)


(b)  A simple model of the hydrogen atom assumes that the wave associated with an electron in the atom is stationary wave as shown in figure given below. The nodes correspond to opposite edges of the atom and the centre of the atom.

Radius of a hydrogen atom = 1.0 x 10^-10 m
The Planck constant, h = 6.6 x 10^-34 Js


      (i)  State the Broglie wavelength of the electron in figure given above.   (1 mark)

     (ii)  Calculate the momentum of an electron in a hydrogen atom.   (2 marks)

    (iii)  The mass of an electron is 9.1 x 10^-31 kg. Calculate the kinetic energy of an electron in a hydrogen atom.   (3 marks)

     (iv)  State and explain briefly where, using this model, the electron in a hydrogen atom is most likely to be found.   (2 marks)

Answer

(a)(i)  Three loops;

(a)(ii)  Coherent waves/waves of same frequency travel opposite direction; superposition;

(b)(i)  λ = 2 x 10^-10 m;

(b)(ii)  λ = h/p; (= 6.6 x 10^-34/2 x 10^-10) = 3.3 x 10^-24 Ns;

(b)(iii)  E_k = p²/2m or momentum = mv and E_k = 1/2 mv²; = (3.3 x 10^-24)²/(2 x 9.1 x 10^-31);
= 6.0 x 10^-18 J;

(b)(iv)  1/2 way out to edge/antinode; probability increases with amplitude;

Questions & Answers (Hints) - 2

Question   (16 marks)

An electric wheelchair powered by a 12 V battery has a maximum speed of 1.5 ms^-1 on level ground. The maximum useful driving power of the motor and transmission system is 30 W. The efficiency of the system is 70%.

(a)  Explain briefly why all modes of transport have a maximum speed which depends on the power output of the propulsion system.   (3 marks)

(b)  For the maximum speed, calculate:

      (i)  the power supplied by the battery;   (2 marks)

     (ii)  the current in the motor circuit.   (2 marks)

(c)  Air resistance is negligible at 1.5 1.5 ms^-1. Show that the resistance due to friction in the moving parts of the wheelchair is 20 N.   (2 marks)

(d)  So that wheelchair users can have access to the same facilities as others, buildings such as schools are fitted with ramps which enable the wheelchairs to be used.

One such ramp has a gradient that rises 0.12 m for every metre moved along the ramp, as shown in the figure below:

The total mass of a wheelchair and a student is 110 kg.
The acceleration of free fall, g = 9.8 ms^-2

      (i)  Calculate the component force in the direction shown by the arrow R because of the weight of the wheelchair and student.   (2 marks)

     (ii)  Assuming that the resistance due to frictional forces is still 20 N, calculate the maximum speed of the wheelchair up the ramp.   (2 marks)

(e)  A designer has to consider a number of physical factors when choosing the material for the ramp when designing it. State and explain briefly two important physical factors which should be considered.

Factor 1:

Factor 2:

  (3 marks)

Answer

(a)  Resistive force increases with speed; work done against this force; speed max. when no resultant force/forces in equilibrium;

(b)(i)  Efficiency = useful output power/input power; P = 30/0.70 = 43 W;


(b)(ii)  Power = VI; I = 43/12 = 3.6 A;

(c)  Power = Fv; F = 30/1.5; (= 20 N)

(d)(i)  F = mg sin θ; (= 110 x 9.81 x 0.12/1) = 129 or 130 N;

(d)(ii)  Total resistive force  = 129 + 20 = 149 N; (power = Fv) v = 30/149 = 0.2(0) ms^-1;

(e)  Strength; support considerable weight; tough; to prevent fracture; thickness; for strength; friction; to get grip; low mass; allow movement to new place; corrosion resistant; to avoid long term problems;