Question

1. write the equation for the impulse-momentum theorem and define all the variables.
2. what is the si unit for impulse?
3. professional boxers wear 8 oz. or 10 oz. gloves depending on the weight class. with the impulse - momentum theorem in mind, describe why boxers use gloves for the safety of themselves and their opponents. use complete sentences to receive full credit.
4. give an example of a system whose mass is not constant?

a. a spinning top
b. a baseball flying through the air
c. a rocket launched from earth
d. a block sliding on a frictionless inclined plane

1. a soccer ball with a mass of 0.4 kg is kicked with a force on 50 n for 0.1 seconds. what is the change in momentum of the ball?
2. a truck with a mass of 2000 kg is traveling at 15 m/s. the driver applies the brakes, exerting a force of 4000 n for 10 seconds. what is the trucks final speed?

Explanation:

Step1: Apply the Impulse - Momentum Theorem

The Impulse - Momentum Theorem states that \(J=\Delta p\). Also, \(J = F\Delta t\) (where \(J\) is impulse, \(F\) is the average force, \(\Delta t\) is the time interval) and \(\Delta p=m\Delta v=mv_f - mv_i\) (where \(\Delta p\) is the change in momentum, \(m\) is the mass of the object, \(v_i\) is the initial velocity, \(v_f\) is the final velocity). For the soccer - ball problem, we use \(J = F\Delta t\) to find \(\Delta p\). Given \(F = 50\ N\) and \(\Delta t=0.1\ s\).

Step2: Calculate the change in momentum

Substitute the values into the formula \(J = F\Delta t\). So, \(\Delta p=F\Delta t=(50\ N)\times(0.1\ s)\)

Step1: Apply the Impulse - Momentum Theorem

We know from the Impulse - Momentum Theorem \(J=\Delta p\) or \(F\Delta t=m(v_f - v_i)\). For the truck problem, \(m = 2000\ kg\), \(v_i = 15\ m/s\), \(F=- 4000\ N\) (negative because it's a braking force), \(\Delta t = 10\ s\)

Step2: Rearrange the formula to solve for \(v_f\)

Starting with \(F\Delta t=m(v_f - v_i)\), we can rewrite it as \(v_f=\frac{F\Delta t}{m}+v_i\)

Step3: Substitute the values

\(v_f=\frac{-4000\ N\times10\ s}{2000\ kg}+15\ m/s\)
First, calculate \(\frac{-4000\times10}{2000}=- 20\ m/s\)
Then \(v_f=-20 + 15\)

Answer:

The change in momentum of the ball is \(5\ kg\cdot m/s\)