Arailroad freight car of mass 3.34 × 104 kg collides with a stationary caboose car. they couple together, and 19.0% of the initial kinetic energy is transferred to thermal energy, sound, vibrations, and so on. find the mass of the caboose.

4.123 * 10∧4 kg

Explanation:

mass of car M' = 3.34 * 10∧4 kg

energy loss E = 19/100  K

from law of conservation of momentum ,

                 M' V' = ( M' + M'' ) v

                        V = M' V' / ( M' + M'' )

       Initial kinetic energy is K'  = (M' V')² / 2

      final kinetic energy  K" = 81 K' /100

                                             =  (M' V')² 81 / (200)     =   ( M' + M'' ) v²/ 2

            therefore , M' / ( M' + M" ) = 0.81

 mass of caboose is ,  M" = 1.234 M' - M'

                                     M" = .234 M'

                                          = 0,234 ( 3.34 * 10∧4 kg)

                                          = 4.123 * 10∧4 kg

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force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.