Learn impulse definition with problems and examples in physics, Practice average force impulse and force time graph, impulse momentum theorem.
\(\overrightarrow{F}_{net}=\dfrac{d\overrightarrow{P}}{dt}\)
\(\displaystyle\int\overrightarrow{F}_{net}.dt=d\overrightarrow{P}\)
\(\displaystyle\int\overrightarrow{F}_{net}.dt=\overrightarrow{\Delta P}\)
\(\displaystyle\int\overrightarrow{F}_{net}.dt=\overrightarrow{P}_f- \overrightarrow{P}_i\)
For e.g., a very hard ball collides with a wall.
\(\displaystyle\int\overrightarrow{F}_{impulsive}.dt=m\overrightarrow{v'}- m\overrightarrow{v}\)
\(\displaystyle\int F_{imp}.dt\)
This quantity is known as Impulse.
\(\displaystyle\int F.dt\) = area under the curve
\(\displaystyle\int F.dt=\Delta P\)
Note : (1) When an impulsive force acts for a short time interval, neglect the effect of finite force for that time interval.
(2) There are situations where forces are not impulsive, but still we can calculate impulse i.e., change in momentum.
A Shaking of hands
B Walking
C Hitting a punching bag
D Chin-up exercise
Impulse \((\overrightarrow{J})=\displaystyle\int\overrightarrow{F}.dt\) ... (1)
From Newton's Second Law
\(\Delta\overrightarrow{P}=\displaystyle\int\overrightarrow{F}.dt\) ... (2)
From (1) and (2)
\(\overrightarrow{J}=\Delta\overrightarrow{P}\)
\(\overrightarrow{P}_f - \overrightarrow{P}_i=\overrightarrow{J}\) ... (3)
A \(10\,\hat i\;m/s\)
B \(6\,\hat i\;m/s\)
C \(5 \,\hat i\;m/s\)
D \(18\,\hat i\;m/s\)
Impulse \((\overrightarrow{J})=\displaystyle\int\overrightarrow{F}.dt\) ... (1)
From Newton's Second Law
\(\Delta\overrightarrow{P}=\displaystyle\int\overrightarrow{F}.dt\) ... (2)
From (1) and (2)
\(\overrightarrow{J}=\Delta\overrightarrow{P}\)
\(\overrightarrow{P}_f - \overrightarrow{P}_i=\overrightarrow{J}\) ... (3)
A \(30\,\hat i\;m/s\)
B \(20\,\hat i\;m/s\)
C \(10\,\hat i\;m/s\)
D \(15 \,\hat i\;m/s\)
Average force can be calculated for the time interval of an impulsive force as discussed below :
We know that
\(\overrightarrow{J}=\displaystyle\int\overrightarrow{F}.dt=\Delta \overrightarrow{P}\)
\(\overrightarrow{F}_{avg}=\dfrac{\Delta\overrightarrow{P}}{\Delta t}\) ... (1)
A Doubled
B Tripled
C Halved
D One-Third
Average force can be calculated for the time interval of an impulsive force as discussed below :
We know that
\(\overrightarrow{J}=\displaystyle\int\overrightarrow{F}.dt=\Delta \overrightarrow{P}\)
\(\overrightarrow{F}_{avg}=\dfrac{\Delta\overrightarrow{P}}{\Delta t}\) ... (1)
Step 1 : Write down final momentum and initial momentum vectors.
Step 2 : Calculate change in momentum
\(\Delta\overrightarrow{P}=\overrightarrow{P}_f - \overrightarrow{P}_i\)
Step 3 : \(\overrightarrow{F}_{avg}=\dfrac{\Delta\overrightarrow{P}}{\Delta t}\)
A \(600\, \hat i\,N\)
B \(-400 \,\hat i\,N\)
C \(100\, \hat i\,N\)
D \(-200\, \hat i\,N\)
\(\overrightarrow{J}=\displaystyle\int\limits_{t_i}^{t_f}\overrightarrow{F}.dt\)
Impulse \((\overrightarrow{J})=\displaystyle\int\overrightarrow{F}.dt\) ... (1)
From Newton's Second Law
\(\Delta\overrightarrow{P}=\displaystyle\int\overrightarrow{F}.dt\) ... (2)
From (1) and (2)
\(\overrightarrow{J}=\Delta\overrightarrow{P}\)
\(\overrightarrow{P}_f - \overrightarrow{P}_i=\overrightarrow{J}\) ... (3)
\(\overrightarrow{J}=\displaystyle\int\limits_{t_i}^{t_f}\overrightarrow{F}.dt\)
A 5 m/sec
B 10 m/sec
C 15 m/sec
D 12 m/sec