
Concept explainers
(a)
The horizontal component of the force.
(a)

Explanation of Solution
Given:
An arch is grounded at the both ends and helium filled balloons are placed at equal interval on the arch with a mass less rope of length
Introduction:
Under equilibrium condition net force acting on a static or a dynamic body sums up to zero. No net force acts on a body under the equilibrium condition.
The arch with the helium filled balloons is in equilibrium. The horizontal component of the force acting on the balloons is of same magnitude.
Write the expression for
Here
Under equilibrium the net force is zero. The horizontal components of the forces are equal in magnitude.
Write the expression of force under equilibrium condition.
Substitute
Conclusion:
Thus, the horizontal component of the forces has equal magnitude.
(b)
The tension of the mass-less rope.
(b)

Explanation of Solution
Given:
An arch is grounded at the both ends and helium filled balloons are placed at equal interval on the arch with a mass less rope of length
Introduction:
The arch with the helium filled balloons is in equilibrium. The horizontal component of the force acting on the balloons is of same magnitude.
Write the expression for Newton’s second law
Here,
Under equilibrium condition all the vertical component of the force balances each other.
Here,
Write the expression for
Under equilibrium condition
Conclusion:
Thus, under equilibrium condition the relation between forces of tension is
(c)
The, trigonometric identity
(c)

Explanation of Solution
Given:
An arch is grounded at the both ends and helium filled balloons are placed at equal interval on the arch with a mass less rope of length
Introduction:
There are two supports at the two ends of the arch. Each supports equally shares the vertical component of the force.
Write the expression for vertical component of the force shared by the two supports.
Here,
Write the expression for the trigonometric identity
Substitute
Write the expression for symmetry of the angle
Here
Write the expression for
Conclusion:
Thus, under equilibrium condition the expression for
(d)
The, trigonometric identity
(d)

Explanation of Solution
Given:
An arch is grounded at the both ends and helium filled balloons are placed at equal interval on the arch with a mass less rope of length
Introduction:
Under equilibrium condition the components of force due to tension of the rope balances each other.
Write the expression for
Substitute
Write the expression for force.
Divide both sides of the above expression by
Rearrange the above equation.
Substitute
Substitute
Write the expression of length of rope between two consecutive balloons.
Here
Write the expression for the horizontal coordinate of the
Write the expression for the vertical coordinate of the
Conclusion:
Thus, the horizontal coordinate of the
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