A classical mechanics problem by Pankaj Joshi

Classical Mechanics Level 5

An object is hanged from ceiling with help of two light strings A & B. Object stays in equilibrium with tension in A & B equal to 40N and 30N respectively. Now the object is pulled by a constant force F=120N perpendicular to the initial plane of object and two strings. If object stays in equilibrium position. Find the tension in string B.

Take $g = 10 m/s^2$

The answer is 78.

1 solution

Ujjwal Rane
Oct 16, 2014

Imgur Imgur When the two strings and the mass hangs in the vertical plane, the two tensions and the weight form a closed force polygon which would be a right angled triangle as shown on the left. This gives the weight of the body as 50 N

After applying the sideways force, the plane of the two strings tilts as shown on right. Here too the three forces form a right angled triangle

Weight 50 N
Sideways force 120 N
A combined tension in A & B of 130 N

The 130 N force will now be contributed by strings A and B in the same ratio. Giving the tension in B as (130)(30/50) = 78 N

How do you get that 130N?

Shubhangi Atre - 6 years, 7 months ago

130N comes from taking the resultant force of 50N and 120N. If two forces are perpendicularly applied, as we can see in the 3rd image of Ujjwal solution , we can use Pytagoras Theorem to find the resultant.

In this case:

$F_{R} = \sqrt{50^{2} + 120^{2}} = 130N$

Jordi Bosch - 6 years, 7 months ago

Why was the ratio 30/50 And how can u say that the ratio will be equal????

Tanish Singhal - 6 years, 3 months ago

Actually the length of the strings matters here At first I took them to be equal........

Aryan Mehra - 6 years, 2 months ago

A classical mechanics problem by Pankaj Joshi

The answer is 78.

1 solution

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