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# Two people pull as hard as they can on horizontal ropes attached to a boat that has a mass of 200 kg. If they pull in th...

Two people pull as hard as they can on horizontal ropes attached to a boat that has a mass of 200 kg. If they pull in the same direction, the boat has an acceleration of 1.52 m/s2 to the right. If they pull in opposite directions, the boat has an acceleration of 0.518 m/s2 to the left. What is the magnitude of the force each person exerts on the boat? Disregard any other horizontal forces on the boat

According to the newton’s law, the force exerted to the left and right can be expressed as,

$\begin{array}{c}F=ma\\ {F}_{right}=\left(200 \mathrm{kg}\right)\left(1.52 \mathrm{m}/{\mathrm{s}}^{2}\right)\\ =304 \mathrm{N}\\ {F}_{left}=\left(200 \mathrm{kg}\right)\left(0.518 \mathrm{m}/{\mathrm{s}}^{2}\right)\\ =103.6 \mathrm{N}\end{array}$

If two people pull in same direction, towards right then net force acting on the boat will be equal to the sum of forces of two people,

If two people pull the boat in opposite direction and the boat move towards left so the force on the left side is greater than the force on the right side. The net force will be the difference of force exerted by first person who is on the left side to the force exerted by second person who is on the right side.

Add above two equations and solve,

$\begin{array}{l}{F}_{1}+{F}_{1}=304 \mathrm{N}+103.6 \mathrm{N}\\ 2{F}_{1}=407.6 \mathrm{N}\\ {F}_{1}=203.8 \mathrm{N}\end{array}$

From equation 1,

$\begin{array}{c}203.8+{F}_{2}=304 \mathrm{N}\\ {F}_{2}=100.2 \mathrm{N}\end{array}$

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