Work, Energy And Power

A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.

Answer Details

T=800N; I=50cm=0.5m,

m=10g=0.01kg

fundamental freq: fo ${\mathrm{<br>}}_{}$ =?

fo ${\mathrm{<br>}}_{}$ = 121√Tμ $\frac{1}{21}<br>$

μ =m1 $\frac{\mathrm{<br>}}{}$=0.010.5 $\frac{0.01}{0.5}$

⇒ fo ${\mathrm{<br>}}_{}$ =12×0.5 $\frac{1}{2\times 0.5}$√8000.02 $\frac{800}{0.02}$

                  fo ${\mathrm{<br>}}_{}$  ⇒√ 40,000

⇒1st overtone = 2fo ${\mathrm{<br>}}_{}$ =2×200 = 400Hz

⇒2nd overtone =3fo ${\mathrm{<br>}}_{}$ =3×200=600Hz

∴3rd over tone= 4fo ${\mathrm{<br>}}_{}$  =4×200=800Hz

You are provided with a battery of e.m.f, E, a standard resistor, R, of resistance 2 Ω $\mathrm{\Omega }$, a key, K, an ammeter, A, a jockey, J, a potentiometer, UV, and some connecting wires.

(i) Measure and record the emf, E, of the battery.

(ii) Set up the circuit as shown in the diagram above with the key open.

(iii) Place the jockey at the point, U, of the potentiometer wire. Close the key and record the reading, i, of the ammeter.

(iv) Place the jockey at a point T on the potentiometer wire UV such that d = UT = 30.0 cm.

(v) Close the circuit, read and record the current, I, on the ammeter,

(vi) Evaluate I1 ${}^1$.

(vi) Repeat the experiment for four other values of d = 40.0 cm, 50.0 cm, 60.0 cm and 70.0 cm. In each case, record I and evaluate I1 ${}^1$.

(vii) Tabulate the results

(ix) Plot a graph with d on the vertical axis and I on the horizontal axis stalling both axes from the origin (0,0).

(x) Determine the slope, s, of the graph.

(xi) From the graph determine the value I1 ${}_1$, of I when d = 0. (ci) Given that=s, calculate 8.

(xii) State two precautions taken to ensure accurate results.

(xii) Given that Eδ $\frac{�}{�}$ = s, calculate δ $�$.

(b)(i) Write down the equation that connects the resistance, R, of a wire and the factors on which it depends. State the meaning of each of the symbols.

(ii) An electric fan draws a current of0.75 A in a 240 V circuit. Calculate the cost of using, the fan for 10 hours if the utility rate is $ 0.50 per kWh.

Answer Details

(a) OBSERVATIONS

(i) Value of E correctly read and recorded to at least 1 d.p in volts.

(ii) Value of i correctly read and recorded to at least 1 d.pin amperes.

(iii) Five values of d correctly determined and recorded to at least 1 d.p in cm.

(iv) Five values of I correctly read and recorded to at least 1 d.p in amperes and in trend.
Trend;  As d increases, I decreases

(v) Five values of I1 ${}^1$ correctly evaluated to at least 3 s.f.

(vi) Composite table showing at least d, I, and I−1 ${}^{-1}$.

(ii) P = IV

Power P = 240×0.75100 $\frac{240\times 0.75}{100}$

0.18kw

Energy consumed in 10hr =  0.18 x 10

= 1.8kWh

Cost of energy = 1.8 x 0.5 = $0.9

OR 

Cost of energy = P x cost x time100 $\frac{\text{<br>}}{}$

0.7×240×101000 $\frac{\mathrm{<br>}}{}$

=  $0.9