How do you calculate impulse using a force-time graph?
The impulse is equal to the area under the force-time graph between the initial and final times.
How do you determine the net external force from a momentum-time graph?
The net external force is equal to the slope of the momentum-time graph at a given point in time.
What are the steps to calculate the change in momentum?
1. Determine the initial momentum ($\vec{p}_0$). 2. Determine the final momentum ($\vec{p}$). 3. Subtract the initial momentum from the final momentum: $\Delta \vec{p}=\vec{p}-\vec{p}_{0}$
How to calculate impulse when the force is a function of time?
1. Identify the net force as a function of time, $\vec{F}_{\text {net }}(t)$. 2. Determine the time interval $[t_1, t_2]$. 3. Integrate the force function over the time interval: $\vec{J}=\int_{t_{1}}^{t_{2}} \vec{F}_{\text {net }}(t) d t$.
How do you apply the impulse-momentum theorem to solve a problem?
1. Identify the impulse acting on the object. 2. Identify the initial and final momentum of the object. 3. Set the impulse equal to the change in momentum: $\vec{J} = \Delta \vec{p}$. 4. Solve for the unknown quantity.
How do you calculate the change in momentum (ฮp)?
1. Determine the final momentum (p). 2. Determine the initial momentum (pโ). 3. Subtract the initial momentum from the final momentum: ฮp = p - pโ.
How do you calculate impulse (J) using the average force and time interval?
1. Determine the average force (F_avg) acting on the object. 2. Determine the time interval (ฮt) over which the force acts. 3. Multiply the average force by the time interval: J = F_avg * ฮt.
How do you determine the net external force from a momentum-time graph?
1. Find the slope of the momentum-time graph at the desired point. 2. The slope represents the net external force at that instant: F_net = ฮp/ฮt.
How do you determine the impulse from a force-time graph?
1. Plot Force vs time on a graph. 2. Calculate the area under the force-time graph. 3. The area represents the total impulse delivered.
How can Newton's Second Law be derived from the Impulse-Momentum Theorem?
1. Start with the Impulse-Momentum Theorem: J = ฮp. 2. Substitute J with F_net * ฮt and ฮp with m * ฮv. 3. Rearrange the equation to get: F_net = m * (ฮv/ฮt) = ma.
What is impulse?
The effect of a force acting over a time interval; a 'push' that changes momentum. Mathematically, it's the integral of force with respect to time: $\vec{J}=\int_{t_{1}}^{t_{2}} \vec{F}_{\text {net }}(t) d t$
Define momentum.
Momentum is a measure of mass in motion; it is a vector quantity defined as the product of an object's mass and its velocity: $\vec{p} = m\vec{v}$
What is the impulse-momentum theorem?
The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum: $\vec{J} = \Delta \vec{p}$
What is net external force?
The vector sum of all forces acting on a system from outside the system. It dictates how quickly the momentum of the system changes.
What is change in momentum?
The difference between the final momentum and the initial momentum of an object: $\Delta \vec{p}=\vec{p}-\vec{p}_{0}$
