Question

Two tugboats are moving a barge. Tugboats $A$ exerts a force of $3000$ newton on the barge. Tugboat $B$ exerts a force of $5000$ newton in the same direction. What is the combined force on the barge?
A) $2000\,N$
B) $8000\,N$
C) $3000\,N$
D) $5000\,N$

Answer 1

Hint: If the two forces act at a point, then the total force is the sum of the forces if they act in the same direction and is the difference in the forces if they both act in a direction opposite to each other. Analyze the terms given and find the combined force on a barge.

Complete step by step solution:
It is given that the
force exerted by the Tugboats $A$ on a barge , ${F_A} = 3000\,N$
Force exerted by the Tugboats $B$ on a barge , ${F_B} = 5000\,N$
It is given that both the tugboats act in the same direction. Since they act in the same direction, they can move a barge with the greater force by the combination of the forces provided by them. Hence the total force on the barge is the sum of the force exerted by the tugboat $A$ and the force exerted by the tugboats $B$.
$\Rightarrow F = {F_A} + {F_B}$
Substituting the force exerted by both the tugboats in the above equation, we get
$\Rightarrow F = 3000 + 5000$
By adding the terms in the right hand side of the equation, we get
$\Rightarrow F = 8000\,N$

Hence the combined force exerted by both the tugboats on the barge is obtained as $8000\,N$.

Thus the option (B) is correct.

Note: If the two forces of the equal magnitude and opposite direction act on the object, then its state remains unchanged. But if there are unbalanced forces acting in the opposite direction, there will be the motion towards greater force. If two forces act in the same direction, the object moves towards the same direction with the greater force equal to its sum.