Supplementary Exercise : Force as a vector

A boat is being towed along the middle of a river 40m wide by men on both banks with ropes of length 80 m each as shown in the diagram. Each rope is pulled with a force of 400N. Find the resultant force acted on the boat.

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Two forces P and Q acts on a small particle. If P=30N, Q=50N, find the magnitude and direction of the resultant when the angle between their directions is:

1. 0°
2. 60°
3. 90°
4. 120°
5. 180°

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A mass of 10N is placed on a smooth plane inclinned at 30° to the horizontal. Find :

1. the force pulling the body down the plane
2. the normal force acted on the plane

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The diagram shows that forces of 5N and 12N acts at right angles on a mass of 10kg which rests on a horizontal plane. Find

1. the resultant force acting on the mass
2. the acceleration produced
3. the distance which the mass moves from rest in 5 seconds.

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A man pulls a 15kg sled along a frictionless level road by a rope inclinde at an angle of 30° with the horizontal. He pulls the rope with a force of 30N. Find

1. the horizontal force that accelerates the sled
2. the acceleration of the sled
3. the force acted by the sled on the road

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A nail is fixed horizontally from a vertical wall and a cord attached to its head at an angle of 30° to the wall with a force of 12N. Find

1. the force (parallel to the wall) tending to bend the nail
2. the force (perpendicular to the wall) tending to pull it out of the wall

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A block of weight 10³N is placed on a plane inclined at 30° to the horizontal. It is connected to a hanging block of weight W by a string passing over a smooth pulley. The friction between the bolck and the plane is 200N.

1. Find the value of W so that the block moves up the plane at constant velocity
2. Find the value of W so that the block moves down the plane at constant velocity

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A heavy stone of mass m kg is suspended by a rope to the ceiling as in the figure. The string is said to be under tension.

1. Mark the direction of the force exerted by the string on the
   1. stone,
   2. ceiling.
2. What should be the tension in N of the string?
3. Will the tension in the string be changed if a boy tries to push the stone to one side as shown in the following figure

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An objet of 5 kg hangs from a fixed point O by a light inextensible string. It is pulled aside by a horizontal force P and is in equilibrium with the string inclined at an angle of 30° to the vertical . Find in N

1. the magnitude fo P,
2. the tension T of the string.

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A small iron ring is placed on a smooth horizontal surface. Three boys pull horizontally on it in different directions. If each boy pulls with a force of 100N, the ring remains at rest.

1. What is the magnitude of the resultant of the pulls?
2. Sketch a view of the ring from above which shows the directions of the pulls.
3. Sketch a force diagram to add up the 3 forces.(tip to tail method).
4. Later, one boy releases the string suddenly while the others pull as before. What is the magnitude and direction of the resultant pull due to the other two boys.

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A picture of mass 1kg can be suspended in three ways as shown. The picture is of uniform density and dimensions (size) 0.5 m × 0.5m.

1. Draw free body diagrams of the picutres in the above cases.
2. If CX=CY =0.5m, find the tension in the strings CX and CY.
3. if DX = DY = 0.26m, find the tension in the strings DX and DY.
4. What is the tension in each of strings AX and BY?
5. How will lengths of AX and BY affect the tensions in them provided that AX=BY?

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