Particle suspended by strings

\includegraphics{figure_2} A particle \(P\) of mass \(1.6\) kg is suspended in equilibrium by two light inextensible strings attached to points \(A\) and \(B\). The strings make angles of \(20°\) and \(40°\) respectively with the horizontal (see diagram). Find the tensions in the two strings. [6]

\includegraphics{figure_2} A block of mass 15 kg hangs in equilibrium below a horizontal ceiling attached to two strings as shown in the diagram. One of the strings is inclined at \(45°\) to the horizontal and the tension in this string is 120 N. The other string is inclined at \(θ°\) to the horizontal and the tension in this string is \(T\) N. Find the values of \(T\) and \(θ\). [6]

\includegraphics{figure_3} A particle \(P\) of mass 0.3 kg is held in equilibrium above a horizontal plane by a force of magnitude 5 N, acting vertically upwards. The particle is attached to two strings \(PA\) and \(PB\) of lengths 0.9 m and 1.2 m respectively. The points \(A\) and \(B\) lie on the plane and angle \(APB = 90°\) (see diagram). Find the tension in each of the strings. [5]

\includegraphics{figure_1} A particle of weight 24 N is held in equilibrium by two light inextensible strings. One string is horizontal. The other string is inclined at an angle of 30° to the horizontal, as shown in Figure 1. The tension in the horizontal string is \(Q\) newtons and the tension in the other string is \(P\) newtons. Find

1. the value of \(P\), [3]
2. the value of \(Q\). [3]

\includegraphics{figure_1} A particle of mass \(m\) kg is attached at \(C\) to two light inextensible strings \(AC\) and \(BC\). The other ends of the strings are attached to fixed points \(A\) and \(B\) on a horizontal ceiling. The particle hangs in equilibrium with \(AC\) and \(BC\) inclined to the horizontal at 30° and 60° respectively, as shown in Figure 1. Given that the tension in \(AC\) is 20 N, find

1. the tension in \(BC\), [4]
2. the value of \(m\). [4]

\includegraphics{figure_1} A particle of weight \(W\) newtons is attached at \(C\) to the ends of two light inextensible strings \(AC\) and \(BC\). The other ends of the strings are attached to two fixed points \(A\) and \(B\) on a horizontal ceiling. The particle hangs in equilibrium with \(AC\) and \(BC\) inclined to the horizontal at \(30°\) and \(60°\) respectively, as shown in Fig. 1. Given the tension in \(AC\) is 50 N, calculate

1. the tension in \(BC\), to 3 significant figures, [3]
2. the value of \(W\). [3]

\includegraphics{figure_1} A particle of weight 8 N is attached at \(C\) to the ends of two light inextensible strings \(AC\) and \(BC\). The other ends, \(A\) and \(B\), are attached to a fixed horizontal ceiling. The particle hangs at rest in equilibrium, with the strings in a vertical plane. The string \(AC\) is inclined at 35° to the horizontal and the string \(BC\) is inclined at 25° to the horizontal, as shown in Figure 1. Find

1. the tension in the string \(AC\),
2. the tension in the string \(BC\).

[8]

\includegraphics{figure_1} A particle has mass \(2\) kg. It is attached at \(B\) to the ends of two light inextensible strings \(AB\) and \(BC\). When the particle hangs in equilibrium, \(AB\) makes an angle of \(30°\) with the vertical, as shown in Fig. 1. The magnitude of the tension in \(BC\) is twice the magnitude of the tension in \(AB\).

1. Find, in degrees to one decimal place, the size of the angle that \(BC\) makes with the vertical. [4]
2. Hence find, to 3 significant figures, the magnitude of the tension in \(AB\). [4]

A small ball \(B\), of mass 0.8 kg, is suspended from a horizontal ceiling by two light inextensible strings. \(B\) is in equilibrium under gravity with both strings inclined at 30° to the horizontal, as shown. \includegraphics{figure_2}

1. Find the tension, in N, in either string. [3 marks]
2. Calculate the magnitude of the least horizontal force that must be applied to \(B\) in this position to cause one string to become slack. [4 marks]

\includegraphics{figure_2} Figure 2 shows a cable car \(C\) of mass 1 tonne which has broken down. The cable car is suspended in equilibrium by two perpendicular cables \(AC\) and \(BC\) which are attached to fixed points \(A\) and \(B\), at the same horizontal level on either side of a valley. The cable \(AC\) is inclined at an angle \(\alpha\) to the horizontal where \(\tan \alpha = \frac{3}{4}\).

1. Show that the tension in the cable \(AC\) is 5880 N and find the tension in the cable \(BC\). [7 marks] A gust of wind then blows along the valley.
2. Explain the effect that this will have on the tension in the two cables. [2 marks]

A particle \(P\), of mass \(m\) kilograms, is attached to one end of a light inextensible string. The other end of this string is held at a fixed position, \(O\). \(P\) hangs freely, in equilibrium, vertically below \(O\). Identify the statement below that correctly describes the tension, \(T\) newtons, in the string as \(m\) varies. Tick (\(\checkmark\)) one box. [1 mark] \(T\) varies along the string, with its greatest value at \(O\) \(\square\) \(T\) varies along the string, with its greatest value at \(P\) \(\square\) \(T = 0\) because the system is in equilibrium \(\square\) \(T\) is directly proportional to \(m\) \(\square\)