Question

a) play the largest player of the red team and leave the blue team empty. hit go. describe the results of the tug of war match using physics terms (i.e. velocity, acceleration, displacement). refer to the sum of forces arrow (aka resultant force vector) in your answer.
b) reset the sim. play the largest player of the each team. hit go. describe the results of the tug of war match using physics terms (i.e. velocity, acceleration, displacement). refer to the sum of forces arrow (aka resultant force vector) in your answer.
c) reset the sim. play the largest player of the blue team. add the two smallest players of the red team one by one. describe what happens as you add each red team member to the sum of forces arrow (aka resultant force vector)

Explanation:

Step1: Analyze case a

When only the largest player of the red - team plays and blue - team is empty, there is a non - zero net force $\vec{F}_{net}$ acting in the direction of the red - team's pull. According to Newton's second law $\vec{F}_{net}=m\vec{a}$, so there will be an acceleration $\vec{a}$ in the direction of the red - team's pull. Initially, the velocity $\vec{v} = 0$. As time $t$ passes, due to the acceleration, the velocity $\vec{v}=\vec{v}_0+\vec{a}t$ (where $\vec{v}_0 = 0$) starts to increase in the direction of the red - team's pull. The displacement $\vec{d}=\vec{v}_0t+\frac{1}{2}\vec{a}t^{2}$ (with $\vec{v}_0 = 0$) also occurs in the direction of the red - team's pull. The resultant force vector points in the direction of the red - team's pull.

Step2: Analyze case b

When the largest player of each team plays, if the forces exerted by the two players are equal in magnitude and opposite in direction, $\vec{F}_{red}=-\vec{F}_{blue}$, then the net force $\vec{F}_{net}=\vec{F}_{red}+\vec{F}_{blue}=0$. According to Newton's first law, an object at rest (the rope and the players before the start) will remain at rest, so the velocity $\vec{v} = 0$, the acceleration $\vec{a}=0$, and the displacement $\vec{d} = 0$. The resultant force vector has a magnitude of 0.

Step3: Analyze case c

When the largest player of the blue - team plays first, there is a force $\vec{F}_{blue}$ in the blue - team's direction. When the first smallest red - team member is added, if $|\vec{F}_{red1}|\lt|\vec{F}_{blue}|$, the net force $\vec{F}_{net}=\vec{F}_{blue}+\vec{F}_{red1}$ still points in the blue - team's direction, but its magnitude decreases compared to when only the blue - team player was playing. When the second smallest red - team member is added, if $|\vec{F}_{red1}| + |\vec{F}_{red2}|\lt|\vec{F}_{blue}|$, the net force still points in the blue - team's direction but is further decreased in magnitude. If $|\vec{F}_{red1}|+|\vec{F}_{red2}| = |\vec{F}_{blue}|$, the net force is 0. If $|\vec{F}_{red1}|+|\vec{F}_{red2}|\gt|\vec{F}_{blue}|$, the net force points in the red - team's direction.

Answer:

a) There is a non - zero acceleration, velocity starts from 0 and increases, displacement occurs in the red - team's direction, and the resultant force vector points in the red - team's direction.
b) Velocity is 0, acceleration is 0, displacement is 0, and the resultant force vector has a magnitude of 0.
c) Initially, the net force points in the blue - team's direction. As red - team members are added, the magnitude of the net force in the blue - team's direction decreases. Depending on the magnitudes of the forces, the net force may become 0 or start pointing in the red - team's direction.