Try to imagine a situation in which the form f=ma would no apply, but the form f=delta p / delta t could be used. Describe that situation. How could you test your prediction.
Could this be a possible answer for the above question.
When catching a ball with bare hands hurts, because it has some force. Since the the ball will always approach one at the same speed, therefore its change in momentum deltaP= Vfinal - Vinitital where Vfinal is zero.
Thus if you allow your hands to move in with the ball as you catch it, you increase the contact time and the total force will be less and hurts less on bare hands.
Since p = mv,
f = dp/dt is equivalent to f = m dv/dt = ma, if the mass is constant
However, mass IS constant for a closed system; so I can't imagine situation with f not equal to m*a.
Total force required to catch a ball is indeed less if you decelerate slowly with a longer contact time. But you have decreased a to decrease f.
f still equals m a
Could the question be true when the mass is not constant, say maybe in the case of cars.
When two cars collide, their masses change but their resultant momentum would be the same before and after the crash so you could you delta p, and the time.
Would that be a possible answer?
One situation in which the equation f=ma would not apply, but the equation f=delta p / delta t could be used is when dealing with relativistic speeds or objects approaching the speed of light.
The equation f=ma, which stands for force equals mass times acceleration, is derived from Newton's second law of motion. It assumes that objects are moving at non-relativistic speeds, where the effects of special relativity are negligible. In this context, mass remains constant, and the equation holds true.
However, at significant fractions of the speed of light, the mass of an object starts to change, according to special relativity. As an object accelerates and approaches the speed of light, its mass increases, and the equation f=ma is no longer valid. Instead, the equation f=delta p / delta t becomes applicable.
The equation f=delta p / delta t relates force (f) to the change in momentum (delta p) over a given change in time (delta t). Momentum (p) is the product of mass and velocity (p=mv), and it remains valid even at relativistic speeds.
To test this prediction, we could design an experiment involving particles with high velocities approaching the speed of light. By measuring the change in momentum over a specific time interval and calculating the force exerted, we can verify if the equation f=delta p / delta t holds true in such relativistic scenarios. This could be done using particle accelerators or other high-energy physics experiments designed to study the behavior of particles at relativistic speeds.