If we jump bare footed on a hard surface,our leg get injured.But they are not injured if you jump on a soft surface like pillow. Explain.
This, we can explain using second law of Newton's law. i.e - Change in angular momentum = Force. Hard surface we can not press much compare to soft surface because gap between the molecules in the hard surface is less compare to soft surface. So change in momentum in hard surface is more because initially there should be some momentum but after interaction with the surface the momentum will suddenly becomes 0. But for the same time interval in soft surface the momentum will not be zero. By 2nd law of Newton's law, we can say Force acts in case of hard surface will be more. So, If we jump hard on the hard surface then it will get injured.
Explain otto (thermodynamic) cycle?
Otto cycle can be explained by the pressure-volume(p-v) diagram. This cycle can be approximated for the petrol(internal combustion engine). It is not the exact p-v diagram for a petrol engine. There are six steps in the cycle : 1.It starts with the intake stroke in which at atmospheric pressure & volume increases. 2. Then, compression stroke, in which the piston compress the working fluid adiabatically & pressure increases.. 3.then, At the end of 2nd stage, combustion start and pressure increases at constant volume. 4.Then, Because of the fuel burn, The work is transfer to the piston & the volume increases adiabatically. 5.Then. at constant volume pressure decreases. 6.And In the last the at constant atmospheric pressure the volume decreases.
\int (1/x(x^4+16))dx =\int(x^-5/(1+16x^-4))dx put 1+16x^-4 = t -64x^-5dx=dt x^-5dx=-dt/64 =\int (-1/64t)dt =(-1/64) Ln(t) + c =(-1/64)Ln(1+16x^-4) + c where,c=constant