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physics Advanced Subsidiary (AS) Level Physics.
 
Solved problems for the chapter:
 

Vector Triangles

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:vector_triangles/5137/


Example 1.

A trolley on the tracks is pulled horizontally with a force of 600 N. The applied force acts at an angle with respect to the direction of the tracks. What component of the force acts in the direction of motion of the trolley?


    
Example 2.

Jack pushes a 30 kg box with a force of 300 N at an angle downwards as shown in the figure. Graphically determine the magnitude of the force component in the direction of motion of the box and the force component directed vertically downwards. With what force does the box act on the ground?


    
3.

A ball weighing 8 N is suspended on a string. It is displaced by an angle (to point A) and allowed to swing.

  • Determine graphically, the forces in the string and in the direction of motion at point A.

  • What are the forces in the string and in the direction of motion when the ball moves through point B?


    
4.

The drawn bow acts on an arrow with a force of 300 N when it is fired. With what force are the limbs of the bow tensioned if the angle between the arrow and each of the limbs is equal to . Solve the problem mathematically with the help of the knowledge of geometry - equilateral triangles.


    
5.

A log is placed on a slope with an inclination of , as shown in the figure. The weight of the log is 5 N. With how much force does the log act perpendicular to the slope and with how much force does it act parallel to the slope?


    
6.

John skis down a slope with an inclination of . His mass is 50 kg. How much force does he apply on the slope while still on the slope?

  • What are the two forces of John on the slope?

  • What are the two forces when he skis on the plain surface?



    
7.

A man strikes a log with an axe with a force of 200 N. With what force does the axe act on both sides of the log? The blade of the axe in the cross section makes an angle of as .


    
8.

A boat is pulled up a stream by two ropes, as shown in the picture. The boat is towed by each rope with a force of 80 N. The angle between the two ropes is . What is the resultant force of both ropes on the boat?


    

9.

A 60 N box is pulled horizontally by a force of 80 N. Graphically determine the magnitude and direction of the resultant force on the box.


    
10.

Two forces 8 N and 6 N are perpendicular to each other as shown in the figure. Their resultant force has also been drawn in the picture. Calculate the size of the resultant force.


    
11.

Three forces of magnitude 4 N each are inclined at to each other, as shown in the figure. What is their resultant force?


    
12.

The figure below shows three forces in a plane, acting at a point. The forces are drawn on a scale of .

  • What is the value of each force?

  • What is the magnitude and direction of the resultant force?


    
13.

Two equal forces are arranged such that their resultant force is equal in magnitude and direction as the two forces. What kind of shape is formed from such arrangement?

    
14.

A tug pulls a ship along a channel with a force of 700 N. By what forces would you have to tow the ship at angles with respect to the direction of movement of the ship in order for the forces to have the same effect on the ship?


    
15.

A ball weighing 600 N hangs from a crane. Determine the direction and magnitude of the force caused by the weight of the ball on the left and right pillars of the crane structure according to the figure below.


    
16.

The wood saw stand (goat) has two legs - see picture. The angle between them is like . We place a log weighing 600 N between the legs. With what force does the log act on each of the legs?


    
17.

Calculate the components and absolute value of the resultant of the vectors (forces) given in the x, y coordinate system in the sketch below.


Forces in x, y coordinate system

    
18.

A boat is tied with ropes to the bank of the river as shown in the picture. Due to the flow of the river, the rope at an angle is tensioned with a force of 600 N. With what force does the river act on the boat?


The boat is tied to the bank with two ropes.

    

19.

A body weighing 6 kg hangs on two ropes attached to the ceiling as shown in the figure. Calculate the forces in both ropes.


Body on two ropes

    
20.

A weight of 10 N is hung in the middle of a rope. What is the force in the left and right arms of the rope when the angle between the two arms of the rope is:





Weight on a rope

    
21.

Two rigid steel beams XY and YZ are fixed at their lower ends and are hinged at Y. Each beam is inclined at to the horizontal, as shown. A weight of hangs from Y. The structure is in equilibrium.




What is the force exerted by each beam on the hinge at Y?









    
22.

Three coplanar forces act on a block. Which diagram shows the directions of the forces such that the block could be in equilibrium?


    
23.

A ladder rests in equilibrium on rough ground against a rough wall.




Its weight W acts through the centre of gravity G. Forces also act on the ladder at P and at Q. These forces are P and Q respectively. Which vector triangle represents the forces on the ladder?


    
24.

A cable car of weight hangs in equilibrium from its cable at point . The cable has tensions and as shown.




Which diagram correctly represents the forces acting at point P?