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In this lesson, we will learn how to find the resultant of a system of parallel coplanar forces and how to locate its point of action.

Q1:

Two parallel forces F ο§ and F ο¨ are acting at two points π΄ and π΅ respectively in a perpendicular direction on β ο© ο© ο© ο© β π΄ π΅ , where π΄ π΅ = 1 0 c m . Their resultant R i j = β 2 0 β 1 6 is acting at the point πΆ that belongs to β ο© ο© ο© ο© β π΄ π΅ . Given that F i j ο¨ = β 3 0 β 2 4 , determine F ο§ and the length of π΅ πΆ .

Q2:

The points π΄ , π΅ , πΆ , π· , and πΈ are lying on the same straight line, where 2 π΄ π΅ = π΅ πΆ = 3 πΆ π· = 6 π· πΈ = 6 c m . Four parallel forces of magnitudes 14, 19, πΉ , and 20 newtons are acting at π΄ , πΆ , π· , and πΈ respectively. If their resultant passes through point π΅ , calculate the magnitude of force πΉ , giving your answer in newtons.

Q3:

Points π΄ , π΅ , πΆ , π· , and πΈ lying in the same straight line, such that π΄ π΅ = 8 c m , π΅ πΆ = 1 8 c m , πΆ π· = 1 2 c m , and π· πΈ = 1 1 c m . Five forces of magnitudes 40, 25, 20, 45, and 50 newtons are acting as shown in the figure. Determine their resultant π and the distance π₯ between its line of action and point π΄ .

Q4:

Three coplanar parallel forces having magnitudes of 6, 8, and πΉ newtons are acting at collinear points π΄ , π΅ , and πΆ respectively. π΄ π΅ = 1 0 c m , and πΆ is not between π΄ and π΅ . The first two forces are acting in opposite directions, and the resultant of the three forces has a magnitude of 6 N, acting in the direction of the second force, with its line of action intersecting ο« π΄ π΅ at a point π· , where π΄ π· = 6 0 c m . Find the magnitude of πΉ and the length of π΅ πΆ .

Q5:

π΄ , π΅ , and πΆ are three points on one straight line, where π΄ π΅ = 6 m , π΄ πΆ = 9 m , and π΅ β π΄ πΆ . Forces of magnitudes 2 N and 2 N are acting vertically downwards at the two points π΄ and πΆ , respectively, and a force having a magnitude of 7 N is acting vertically upwards at the point π΅ . Find the magnitude and direction of the resultant π and the distance π₯ of its point of action from the point π΄ .

Q6:

π΄ , π΅ , πΆ , π· , and πΈ are five points on the same straight line, where π΄ π΅ = 2 0 c m , π΅ πΆ = 6 c m , πΆ π· = 8 c m , and π· πΈ = 5 c m . Forces of magnitudes 4, πΉ , and 10 newtons are acting vertically downwards at the points π΄ , πΆ , and πΈ respectively, and forces of magnitudes 7 and πΎ newtons are acting vertically upwards at π΅ and π· respectively. Given that the resultant of the forces is 3 N, and it is acting vertically downwards at the point π , where π β π΄ πΈ and π΄ π = 1 4 c m , determine the values of πΉ and πΎ .

Q7:

Four parallel forces of magnitudes 6, 3, 8, and 2 kg-wt are acting perpendicularly in the same direction on the points π΄ , π΅ , πΆ , and π· respectively. Given that the four points are on the same straight line, where π΄ π΅ = π΅ πΆ = 8 9 c m and πΆ π· = 1 0 7 c m , determine the magnitude and direction of the resultant force and the distance π₯ between the resultantβs point of action on the straight line and π΄ .

Q8:

Parallel forces β πΉ 1 , β πΉ 2 , β πΉ 3 , and β πΉ 4 act at the points π΄ ( β 1 0 , 4 ) , π΅ ( 9 , 4 ) , πΆ ( β 7 , 7 ) , and π· ( β 3 , 1 ) , respectively, where the forces are in equilibrium. Given that β πΉ = 3 β π + β π 1 and β β β πΉ β β = 2 β 1 0 2 N, and they act in the opposite direction of β πΉ 1 , find each of β πΉ 2 , β πΉ 3 , and β πΉ 4 .

Q9:

A uniform rod π΄ π΅ having a weight of 64 N and a length of 168 cm is resting horizontally on two identical supports at its ends. A weight of magnitude 56 N is suspended at a point on the rod that is π₯ cm away from π΄ . If the magnitude of the reaction at π΄ is double that at π΅ , determine the value of π₯ .

Q10:

A uniform rod having a weight of 35 N is resting horizontally on two supports π΄ and π΅ at its ends, where the distance between the supports is 48 cm. If a weight of magnitude 24 N is suspended at a point that is 38 cm away from π΄ , determine the reactions of the two supports π π΄ and π π΅ .

Q11:

A non-uniform rod π΄ π΅ having a weight of 40 N and a length of 80 cm is suspended vertically from its midpoint by a light string, and it becomes in equilibrium in a horizontal position when a weight of magnitude 29 N is suspended from its end π΄ . Determine the distance π₯ between the point at which the weight of the rod is acting and end π΄ . After removing the weight at π΄ , determine the magnitude of the vertical force that would be needed to keep the rod in equilibrium in a horizontal position when it acts at end π΅ .

Q12:

A uniform rod π΄ π΅ having a length of 1.3 m and weighing 147 N is resting in a horizontal position on two supports, where the support πΆ is at the end π΄ , and π· is at a distance π₯ from the end π΅ . Find the reaction of the support π πΆ and the distance π₯ , given that π = 2 5 π πΆ π· .

Q13:

A uniform rod weighs 15 N and has a length of 90 cm. It is suspended from its ends by two vertical strings, where is the tension of the string at , and is the tension of the string at . A weight of 14 N is suspended from the rod, 30 cm away from , and a weight of 27 N and is suspended from the rod, 30 cm away from . Determine the values of and .

Q14:

π΄ π΅ is a uniform rod having a length of 111 cm and weighing 78 N. The rod is suspended horizontally from its ends π΄ and π΅ by two vertical strings. Given that a weight of 111 N is suspended π₯ cm away from the end π΄ so that the tension at π΄ is twice that at π΅ , determine the tension at π΅ and the value of π₯ .

Q15:

π΄ π΅ is a uniform rod having a length of 78 cm and weighing 155 N. The rod is resting horizontally on two supports, π΄ and πΆ , where πΆ is 13 cm away from π΅ . Determine the minimum weight π€ to be suspended at π΅ so that there is no pressure at π΄ , and find out the pressure on πΆ at that instant.

Q16:

π΄ π΅ is a uniform rod with length 48 cm and weight 20 kg-wt. It rests in a horizontal position on two supports, πΆ and π· , that are 6 cm and 12 cm away from π΄ and π΅ , respectively. A weight of magnitude 26 kg-wt is suspended from the rod at a point 12 cm away from π΄ . Another weight of 16 kg-wt is suspended from the rod, 18 cm away from π΅ . Calculate the size of the reaction forces, π πΆ and π π· , at πΆ and π· respectively.

Q17:

A uniform rod π΄ π΅ having a weight of 30 N and a length of 190 cm is resting horizontally on two supports πΆ and π· , where πΆ is near to π΅ , and π· is near to π΄ . If the pressure on πΆ is double that on π· , where the distance between them is 66 cm, determine the lengths of πΆ π΅ and π΄ π· .

Q18:

A uniform rod having a length of 114 cm and a weight of 66 N is suspended horizontally by means of two vertical strings at its ends. The greatest tension each string can handle is 87 N. If a weight of 76 N is to be attached to the rod, find the minimum distance at which it can be hung away from the string that has the maximum tension.

Q19:

The length of a rod π΄ π΅ is 111 cm, and its weight is 95 newtons, which is acting at its midpoint. The rod is resting horizontally on two supports, where one of them is at end π΄ , and the other is at a point πΆ which is 30 cm away from π΅ . A weight of 71 newtons is suspended from the rod at a point that is 9 cm away from π΅ . Find the magnitude of weight π€ that should be suspended from end π΅ so that the rod is about to rotate, and determine the value of the pressure π exerted on πΆ in that situation.

Q20:

π΄ π΅ is a uniform rod of length 93 cm and weight 35 newtons. It is suspended horizontally by two vertical strings from its two ends π΄ and π΅ . Determine the distance from π΄ in cm that a weight of 125 newtons should be suspended for the tension magnitude at π΄ to be twice its magnitude at π΅ .

Q21:

A uniform rod having a length of 56 cm and weighing 38 N is resting horizontally by means of a support and a string. Given that the support is at the end and the string is 11 cm away from the end , determine the stringβs tension and the supportβs reaction .

Q22:

π΄ π΅ is a rod having a length 120 cm and weighing 12 N, which is acting at a point 15 cm away from π΄ . Given that the rod is resting on a support at its midpoint, determine the reaction of the support π , and find the weight π that should be suspended from the end π΅ to make the rod in equilibrium in a horizontal position.

Q23:

Jennifer lay on a horizontal uniform wooden plank of length 3.6 m and weight 19 kg-wt that was fixed at each end on two supports π΄ and π΅ . Given that the reactions of the two supports π΄ and π΅ are 49 kg-wt and 52 kg-wt, respectively, determine the distance between the point of action of her weight and support π΄ .

Q24:

A non-uniform wooden board π΄ π΅ , having a length of 16 m, is resting horizontally on two supports at πΆ and π· such that π΄ πΆ = 3 m and π΅ π· = 4 m . If the maximum distance that a man, whose weight is 639 N, can move on the board from π΄ to π΅ without getting the board imbalanced is 14.2 m, and the maximum distance the same man can move from π΅ to π΄ is 14.8 m, find the weight π€ of the board and the distance π₯ between its line of action and the point π΄ .

Q25:

A uniform iron beam having a weight of 56 N and a length of 100 cm is resting horizontally on two supports π΄ and π΅ , where π΄ is at the end of the beam, and π΅ is 44 cm away from the other end. Determine the reactions of the supports π π΄ and π π΅ .

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