PASCO TD-8551A MECHANICAL EQUIVALENT OF HEAT - Manual (Page 10)

Mechanical Equivalent of Heat 012-04331E
6
Calculations
Calculating W, the Work Performed
The work performed on the cylinder by turning the crank equals
τ
, the torque acting on
the cylinder, times
θ
, the total angle through which the torque acts. It would be difficult
to directly measure the torque delivered by the crank. However, since the motion of the
cylinder is more or less constant through the experiment, we know that the torque
provided by the crank must just balance the torque provided by the friction from the
rope. The torque provided by the rope friction is easily calculated. It is just:
τ
= MgR
where M is the mass hanging from the rope, g is the acceleration due to gravity, and R is the
radius of the cylinder.
Each time the crank is turned one full turn, this torque is applied to the cylinder through an
angle 2
π
. The total work performed therefore is:
W =
τθ
= MgR (2
π
N);
where M is the mass hanging from the rope;
g is the acceleration due to gravity (9.8 m/s
2 );
R is the radius of the aluminum cylinder;
and N is the total number of times the crank was turned.
Calculating Q, the Heat produced
The heat (Q) produced by friction against the aluminum cylinder can be determined from the
measured temperature change that occurred. The calculation is:
Q = m c (T
f
- T
i
);
where m is the mass of the aluminum cylinder;
c is the specific heat of aluminum (0.220 cal/gC
∞
);
T
f
is the final temperature of the cylinder;
and T
i
is the initial temperature of the cylinder, just before cranking.
Calculating J, the Mechanical Equivalent of Heat
J is just the ratio of the work performed to the heat produced. Therefore:
J = W/Q