Question

51) A spacecraft traveling out of the solar system at a speed of 0.95c sends back information at a rate of 1400 kHz. At what rate do we receive the information?

57) Newton’s second law is given by F=dp/dt. If the force is always parallel to the velocity, show that F=ma.

70) What is the speed of a proton when its kinetic energy is equal to twice its rest energy?

75) How much mass-energy (in joules) is contained in a peanut weighing 0.1 ounce? How much mass-energy do you gain by eating 10 ounces of peanuts? Compare this with the food energy content of peanuts, about 100 kcal per ounce.

Answer 1

Answer 57:

Newton's second law is give by F= dp/dt where

p = momentum or m X v (mass times velocity). So let's substitute p = m X v (cross product of mass and velocity) in the above equation.

So,

F = d (m x v)/dt

F = v.dm/dt + m.dv/dt (this is how expansion of differentiated cross product looks like)

since m is constant of a particle here, the rate of change of mass with respect to time or dm/dt = 0. So, v.dm/dt = 0.

So,

F = m.dv/dt

Now, since the force is always in the direction of velocity (this means that direction will not change and rate of change of velocity with respect to time can be written as 'acceleration' or 'a'.

So,

F= m.a

or

F = ma