Chapter 3.2, Problem 1cT

Use Newton's second law and the definition of acceleration to derive an equation for each cart relating the net force on the chart to the change in velocity of the cart $\left(\Delta {\stackrel{\to }{\upsilon }}_A\text{or}\Delta {\stackrel{\to }{\upsilon }}_B\right)$ and the time interval $\left(\Delta t_A\text{or}\Delta t_B\right)$ that the cart spends between the two marks.

1. Is the quantity $m_A\left|\Delta {\stackrel{\to }{\upsilon }}_A\right|$ greater than, less than, or equal to $m_B\left|\Delta {\stackrel{\to }{\upsilon }}_B\right|$ ? Explain how you can tell.

For a constant net force, the quantity ${\stackrel{\to }{F}}_{\text{net}}\Delta t$ is called the impulse imparted to the object.

2. Is the magnitude of the impulse imparted to cart A greater than, less than, or equal to the magnitude of the impulse imparted to cart B? Explain your reasoning.

3. Write an equation showing how the impulse imparted to cart A is related to the change in momentum vector of cart $A\left(\Delta {\stackrel{\to }{p}}_A\right)$ , where momentum, denoted by $\stackrel{\to }{p}$ , is the product of the mass and velocity of the object.

This relationship is known as the impulse-momentum theorem.

4. Is the magnitude of the final momentum of cart $A\left(\Delta {\stackrel{\to }{p}}_{A_t}\right)$ greater than, less than or equal to the magnitude of the final momentum of cart $B\left(\Delta {\stackrel{\to }{p}}_{B_s}\right)$ ? Explain.