PRE-LAB 1) A schematic of the experimental set-up is shown in Fig. 1. A flat cor

Question

PRE-LAB 1) A schematic of the experimental set-up is shown in Fig. 1. A flat cord is wrapped around horizontally mounted aluminum cylinder. A mass M is suspended from one end of the caa You will initially hold the other end to keep the cord from slipping. As the drum is tune frictional force between the cord and the drum produces thermal energy that heats apparatus. The temperature of the apparatus is determined by a thermistor inside the cylinds 2) Use a free body diagram to show that the weight of the suspended mass is equal and oppositath the force of your hand on the cord plus the total frictional force between the cord and the dnm up the Use the resulting equation to show that the force of friction is equal to the weight of the mass if the drum is turned at a rate such that the force of your hand can be neglected. FRI CTI ON ROPE If N is the number of rotations of the cylinder, C is the circumference of the cylinder, m is its mass, and g is the acceleration due to gravity, derive an expression for the total mechanical work performed. HANGI NG MASS Fig. 1. Schematic of the apparatus

Explanation / Answer

as we can see, mechanical work done by the tension in the rope = heat energy produced

now, tension in the rope = T = Mg

work done by tension = T*N*C [ where N is number of loops of rope and C is the circumference of the pulley]

let the temperature change of the pulley be dT and its heat capacity in cal/ gC be c and mass be m

then for conversion factor k

TNC = kmcdT

k = TNC/mcdT

also. T = Mg

hence from the data

M N C m c d k

brass 5 130 0.15 50 0.292 16 4.094499144

aluminium 4 52 0.2 25 0.215 18 4.218046512

copper 5 45 0.12 34 0.0924 20 4.21552712

steel 4 40 0.18 30 0.11 20 4.280727273

brass 6 92 0.14 35 0.292 18 4.12109589

so mean conversion factor form joules to cal = 4.185979188

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