Frictional mechanical clutch slip(dry clutch)

[marellasunny]

During the short period of engagement of the friction clutch(say t=1sec),energy is obviously lost as heat.I've been asked to calculate this loss of heat by my teacher.

I've been given:
1.Input power(engine)= 50kW
2.Slip decreases linearly with time
3.Engagement process time,t=1sec

Now,I know how to go about solving the problem. It involves integration of the following eq.:

$$Heat loss=\int_{0second}^{1 second}P_{loss}.dt$$

But,the question is related to the slip of the clutch.Is the slip of the clutch equal to 1 at time t=0(i.e when I start releasing my foot from the clutch pedal and the pressure plate just starts to scrape the flywheel plate)? So,if I were to draw a graph of the slip 's' on the y-axis and time of engagement 't' on the x-axis,I would be drawing a straight line with a negative slope. Also,would the clutch slip when its fully engaged?

This is the equation of slip as a function of engine speeds(THIS I UNDERSTAND):
$$slip=\frac{n_{engine}-n_{output/clutch pressure plate}}{n_{engine}}$$

This is the equation of the slip as a function of the engagement time(I DO NOT KNOW WHAT TO PLUG IN HERE):
$$s=-\frac{ds}{dt}t+c$$

s-slip
c-intercept on slip axis (IS c=1??)

 

[rcgldr]

Is the slip of the clutch equal to 1 at time t=0?

For the slip equation you wrote, slip = 1 if the car is not moving. I don't know how this helps in calculating heat loss.

An alternative would be to calculate energy output from the engine versus energy gained by the car from initial start with clutch slipping to the time when the clutch stops slipping. With light throttle application and clutch slippage only until a relatively slow speed, the energy loss would be small. With heavy throttle application and clutch slippage until high speed, the energy loss would be much greater.