A particle of mass kilogram hangs from a string that is attached to a fixed point. The particle is acted on by a horizontal force of magnitude newtons. The system is in equilibrium when the string makes an angle to the horizontal, as shown in the diagram below. The tension in the string has magnitude newtons.
 

The value of    is

1. A light inextensible string is connected at each end to a horizontal ceiling. A mass of kilograms hangs in equilibrium from a smooth ring on the string, as shown in the diagram below. The string makes an angle with the ceiling.
     
   
    
   Express the tension, newtons, in the string in terms of , and .  (1 mark)
2. A different light inextensible sting is connected at each end to a horizontal ceiling. A mass of kilograms hangs from a smooth ring on the string. A horizontal force of newtons is applied to the ring. The tension in the sting has a constant magnitude and the system is in equilibrium. At one end the string makes an angle with the ceiling and at the other end the string makes an angle with the ceiling, as shown in the diagram below.
    
   
    
   Show that  .  (3 marks)

A 12 kg mass is suspended in equilibrium from a horizontal ceiling by two identical light strings. Each string makes an angle of 60° with the ceiling, as shown.
 

The magnitude, in newtons, of the tension in each string is equal to

A.     

B.   

C.   

D.   

E.  

A flowerpot of mass kg is held in equilibrium by two light ropes, both of which are connected to a ceiling. The first rope makes an angle of 30° to the vertical and has tension newtons. The second makes an angle of 60° to the vertical and has tension newtons.
 

1. Show that   (1 mark)
2. The first rope is strong, but the second rope will break if the tension in it exceeds 98 newtons.

    

   Find the maximum value of for which the flowerpot will remain in equilibrium.  (3 marks)

Forces of magnitude 5 N, 7 N and N act on a particle that is in equilibrium, as shown in the diagram below.
 

The magnitude of , in newtons, can be found by evaluating

A.  

B.  

C.  

D.  

E.  

The diagram above shows a mass suspended in equilibrium by two light strings that make angles of and with a ceiling. The tensions in the strings are and , and the weight force acting on the mass is . The correct statement relating the given forces is

A.  

B.  

C.  

D.  

E.   

Two light strings of length 4 m and 3 m connect a mass to a horizontal bar, as shown below

The strings are attached to the horizontal bar 5 m apart.
 

Given the tension in the longer string is    and the tension in the shorter string is  ,  the ratio of the tensions    is

A.  

B.   

C.   

D.   

E.   

A taut rope of length m suspends a mass of 20 kg from a fixed point . A horizontal force of newtons displaces the mass by 1 m horizontally so that the taut rope is then at an angle of    to the vertical.

1. Show all the forces acting on the mass on the diagram below.  (1 mark)

2. Show that  .  (1 mark)
3. Find the magnitude of the tension force in the rope in newtons.  (2 marks)

A body of mass 5 kg is held in equilibrium by two light inextensible strings. One string is attached to a ceiling at and the other to a wall at . The string attached to the ceiling is at an angle to the vertical and has tension newtons, and the other string is horizontal and has tension newtons. Both strings are made of the same material.

1. i. Resolve the forces on the body vertically and horizontally, and express in terms of  .  (2 marks)
2. ii. Express in terms of  .  (1 mark)
2.  Show that    for  .  (1 mark)
3.  The type of string used will break if it is subjected to a tension of more than 98 N.

    

    Find the maximum allowable value of    so that neither string will break.  (3 marks)

The diagram below shows a mass being acted on by a number of forces whose magnitudes are labelled. All forces are measured in newtons and the system is in equilibrium.
 

The value of is

A.   

B.