2.3. Dynamics term

Try these first

1. 1.

   Define linear momentum in mechanics.

   Hint

   Think about what happens when you multiply mass by speed.

2. 2.

   What does density represent?

   Hint

   Consider how dense materials feel compared to lighter ones.

3. 3.

   What defines linear momentum?

   • Mass and velocity
   • Force and time
   • Density and pressure

   Hint

   Consider the formula \\(p = mv\\).

4. 4.

   True or False: Density remains constant in a deforming body.

   • True
   • False

   Hint

   Think about how materials react under stress.

5. 5.

   A material has a density that varies linearly with position, $\rho(x) = 5 + x$. Calculate the total linear momentum if the volume of the material is $V = 10$ and it moves with a velocity of $v = 2$.

   Hint

   Break the calculation into components focusing on how density varies with position.

6. 6.

   Explain how the varying density impacts the rate of change of momentum for a cylindrical rod of length $L$ compressed under a force.

   Hint

   Consider the integration of the density and how it contributes to overall momentum change.