If I take a glob of mud and throw it against a wall with the speed of V and stops in time T and than I take a ball and throw it and it hits the wall with speed V and leaves the wall a time T later at a speed of 0.5V and they both have same value and mass, which one involves a greater total force on the object.
I think it is the ball but to be honest I don't understand why-
Could you give me some direction, please?
physics question here.
need physics help
need physics help here.
Force is the rate of change of momentum, equal to mass*velocity.
Both objects hit the wall and the change of velocity (and hence momentum) takes place in time T.
In the case of the mud-pie, the rate of change of momentum is m(0-V)/T = -mV/T, since the final velocity is 0 (inelastic impact).
In the case of the bass, the rebound velocity is 0.5V, hence the change of momentum is m(-0.5V-V)/T=-1.5mV/T.
Thus we conclude that the absolute value of the force on the wall is greater in the case of the__________.
To determine which object involves a greater total force, we need to analyze the change in momentum for each object.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). The change in momentum (∆p) is equal to the final momentum (p-final) minus the initial momentum (p-initial).
For the mud glob:
Initial momentum (p-initial) = mass (m) × velocity (V) = mV
Final momentum (p-final) = mass (m) × velocity (0) = m × 0 = 0
Change in momentum (∆p) = p-final - p-initial = 0 - mV = -mV
Since the mud glob stops completely, its final momentum is zero, and the change in momentum is negative.
For the ball:
Initial momentum (p-initial) = mass (m) × velocity (V) = mV
Final momentum (p-final) = mass (m) × velocity (0.5V) = 0.5mV
Change in momentum (∆p) = p-final - p-initial = 0.5mV - mV = -0.5mV
Here, the change in momentum is also negative, but the magnitude (absolute value) of the change is greater compared to the mud glob (∆p of the ball is 0.5mV, while ∆p of the mud glob is mV).
Using Newton's second law, force (F) is defined as the rate of change of momentum (∆p) over time (T): F = ∆p / T. Thus, if the magnitude of the change in momentum (∆p) is greater, it means the force (F) exerted is also greater.
Therefore, the ball experiences a greater total force than the mud glob, as the magnitude of its change in momentum is larger.
In summary, although both objects experience a negative change in momentum, the ball involves a greater total force because its change in momentum is larger in magnitude.