Chapter 4, Problem 13Q

To determine

What factor and which team will win the tug of war according to Newton’s law of motion.

Answer to Problem 13Q

Solution:

Friction force. The team with more friction with the surface will win.

Explanation of Solution

In a tug of war, the team that pushes hardest against the ground wins the game. According to given statement, it is true that both teams apply the same force on rope due to the tension in the rope. But the winning team will have more friction and thus the ground pushes harder on the winning team, making a net unbalanced force.

The forces on the rope must be equal and opposite by Newton’s third law but not all forces acting on each team are such action-reaction pairs. The friction between one team and the ground does not match with the other team. Friction can be larger on one side than on the other. In addition, the grips on the rope need not be equal and opposite.

LetF_1Gbe the force on team 1 from the ground,

F_2G is the force on team 2 from the ground

F_T1R, the force on the rope team 1(Tension)

F_T2R, the force on the rope team 2(Tension)

Thus, the net force on the winning team is

F_1G Large force from the ground

F_2G Small force from the ground

From free body diagram

$F_{1G}-F_{T1R}\gg F_{2G}-F_{T2R}$

The forces on the rope are equal i.e.F_T1R = F_T2R

$F_{1G}\gg F_{2G}$

From this, the winning team would have put force on the ground.