02-Numerical Problems

“Laws of Forces” Numerical Problems

Try to solve the following “Laws of Forces” numerical problems to clear the concepts in solving the numerical problems.

First of all go to the theory portion of the respective topic and then try to solve the numerical problems by yourself. If facing problem in solving the numerical, click on the Go to solution button to see the ready made solution placed at the bottom of each numerical problem.

01) PROBLEM – P020101

The resultant of two forces is $( 8 \ kgwt )$ and its direction is inclined at $60 \degree$ to one of the forces whose magnitude is $( 4 \ kgwt )$ .

Find magnitude and direction of the other force.

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Parallelogram law of addition of forces.

02) PROBLEM – P020102

Find a point within a quadrilateral as shown in figure such that if it is acted upon by forces represented by lines joining the point to the angular points of the quadrilateral, it will be in equilibrium.

RESULTANT OF MANY FORCES — PROBLEM FIGURE P020102

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03) PROBLEM – P020103

A string $ACB$ of length $( 47.3 \ cm )$ is tied to two points A and B at the same level as shown in figure. A smooth ring of weight $( 40 \ kg )$ which can freely slide along the string is at C at $( 30 \ cm )$ away from A along the string and is pulled by a horizontal force $( P )$ .

RESOLVING FORCES IN COMPONENTS — PROBLEM FIGURE P020103

If point C is $( 15 \ cm )$ below the level of AB, determine the magnitude of force $( P )$ .

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04) PROBLEM – P020104

Two identical prismatic bars $PQ$ and $RS$ each weighing $( 15 \ kg )$ are welded to form a Tee $( T )$ and are suspended in a vertical plane as shown in figure.

EQUILIBRIUM OF TEE BAR — PROBLEM FIGURE P020104

Calculate the value of angle $( \theta )$ that the bar $PQ$ will make with vertical when a vertical load of $( 20 \ kg )$ is applied at point S.

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Moment of a force.

05) PROBLEM – P020105

Figure below shows a body under the action of co-planar forces.

RESULTANT OF CO-PLANER FORCES — PROBLEM FIGURE P020105

Determine the magnitude, direction and position of a single force which will keep the body in equilibrium.

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06) PROBLEM – P020106

Find the value of the angle $( \theta )$ in figure if block $B$ is about to slide.

BLOCK ON INCLINED PLANE — PROBLEM FIGURE P020106

Weight of block $A$ is $( 10 \ kg )$ and that of the block $B$ is $( 20 \ kg )$ and $( \mu = 0.25 )$ for all surfaces.

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07) PROBLEM – P020107

A block of weight $( W_1 = 100 \ kgf )$ rests on a horizontal surface and supports on top of it another block of weight $( W_2 = 25 \ kgf )$ as shown in figure.

FRICTION ON A BLOCK ON HORIZONTAL PLANE — PROBLEM FIGURE P020107

The block $W_2$ is attached to a vertical wall by an inclined string $AB$ . Find the magnitude of the horizontal force $( P )$ applied to the lower block as shown that will be necessary to cause slipping to impend. The coefficient of static friction for all surfaces is $( \mu = 0.3 )$

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08) PROBLEM – P020108

A uniform rod of length $( 10 \ cm )$ is placed with one end inside a smooth hemispherical bowl. Axis of bowl is vertical and radius is $( 4 \ cm )$ .

A ROD KEPT IN A SMOOTH HEMISPHERICAL BOWL — PROBLEM FIGURE P020108

Find the inclination of the rod to the horizontal and the length which projects out of the bowl.

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09) PROBLEM – P020109

A uniform wheel of $( 1000 \ kg )$ weight and $( 60 \ cm )$ in diameter rests against a rigid rectangular block of $( 15 \ cm )$ height as shown in figure.

FRICTION OF WHEEL ON BLOCK — PROBLEM FIGURE P020109

Find the least pull through the centre of the wheel to just turn the wheel over the corner of the block. All surfaces are smooth. Also find the reaction of the block.

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10) PROBLEM – P020110

Find the maximum tension in the cord shown in figure, if the bodies have developed full friction.

MAXIMUM TENSION IN CORD WHEN BODIES HAVE DEVELOPED FULL FRICTION — PROBLEM FIGURE P020110

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11) PROBLEM – P020111

Two blocks which are connected by a horizontal link are supported on two rough planes as shown in figure.

FRICTION ON BLOCKS ON ROUGH PLANES — PROBLEM FIGURE P020111

The coefficient of friction for block $A$ is $( 0.4 )$ . The angle of friction for the block $B$ on the inclined plane is $( \phi = 20 \degree )$ . Find the smallest weight $( W_1 )$ of the block $A$ for which equilibrium can exist.