Friction

If an object just begins to slide on a surface inclined at 30º to the horizontal,the coefficient of friction is?

Answer Details

The coefficient of friction is a number that represents the resistance to motion between two objects in contact. It is determined by the properties of the surfaces in contact and the force pressing them together. When an object just begins to slide on a surface inclined at 30º to the horizontal, the coefficient of friction can be calculated using the formula: friction = μ * normal force where μ is the coefficient of friction and normal force is the force perpendicular to the surface. In this case, the normal force is equal to the weight of the object, which is given by the formula: normal force = object weight * cos(30º) Combining these two formulas, we can calculate the coefficient of friction: friction = μ * object weight * cos(30º) Since the object is just beginning to slide, the friction force is equal to the force needed to start the slide, which is the gravitational force acting on the object down the incline. Therefore, we can set these two equal: friction = object weight * sin(30º) Solving for μ, we get: μ = friction / (object weight * cos(30º)) = sin(30º) / cos(30º) = 1/√3 So, the coefficient of friction for an object just beginning to slide on a surface inclined at 30º to the horizontal is 1/√3.

You are provided with a battery of e.m.f, E, a standard resistor, R, of resistance 2 ? $\mathrm{?}$, 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 E? $\frac{\mathrm{<br>\; <span\; style="font-size:\; var(--bs-body-font-size);\; font-weight:\; var(--bs-body-font-weight);\; word-spacing:\; normal;"><br></span>}}{}$ = s, calculate ??
.

(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 $\frac{\text{P x cost x time}}{100}$

0.7×240×101000 $\frac{0.7\times 240\times 10}{1000}$

=  $0.9