Unit 1: Mathematics for engineering
LO3: Understand exponentials and logarithms related
to engineering problems
Inverse function and log laws
Activity 1
The power transmitted by a pulley and belt is
given by:
P = v (F1 – F2) watts
When the belt just starts to slip, the force ratio is:
F1/F2 = e
Where:
v = velocity of the belt (ms-1)
F1 and F2 = tensions in the belt (N)
 = the coefficient of friction between the belt
and the pulley
 = angle of wrap (angle of contact between belt
and pulley) (radians)
For the belt and pulley system shown above, when running the belt velocity is 18.85 m/s. Tension in the
belt when running (F1) is 157.4 N and the power transmitted is 1786 W. Coefficient of friction () is 0.32.
Determine (just at the point of slipping):
(a) Tension in the belt (F2) when running
(b) The angle of wrap (angle of contact) between the belt and the pulley in degrees.
Version 1
Activity 2
Charging the voltage across a capacitor (at any time
(t)) is given by the formula:
VC = VS (1 – e-t/RC)
Where:
VC = voltage across the capacitor (volts)
VS = supply voltage (volts)
t = time (seconds)
R = value of resistor (ohms)
C = value of capacitor (farads)
In a circuit consisting of a series resistor and capacitor, the supply voltage is 9 V. The value of the
resistor is 470 k, and when charging at t = 100 s the voltage across the capacitor is 7.93 V.
Determine the value of the capacitor in the circuit.
Version 1