contestada

A metal ball of mass 2 kg is supported by a massless inextensible string, 12 cm long. A horizontal force displaces the ball by 30oto the vertical so that the string remains taut. Find:a) the horizontal force.b) the tension in the thread.

Respuesta :

As it is given that 2 kg mass is suspended by 12 cm long thread and then a horizontal force is applied on it so that it remains in equilibrium at 30 degree angle

So here we can use force balance in X and Y directions

now for X direction or horizontal direction we can use

[tex]F = Tsin30[/tex]

for vertical direction similarly we can say

[tex]mg = T cos30[/tex]

so here we first divide the two equations

[tex]\frac{F}{mg} = \frac{sin 30}{cos 30}[/tex]

[tex]\frac{F}{mg} = tan 30[/tex]

[tex]F = mg tan30[/tex]

now plug in all values in the above equation

[tex]F = 2 * 9.8 * tan30[/tex]

[tex]F = 11.3 N[/tex]

Part b)

now in order to find the tension in the thread we can use any above equation

[tex]F = T sin30[/tex]

[tex]11.3 = T sin30[/tex]

[tex]T = \frac{11.3}{sin30}[/tex]

[tex]T = 22.6 N[/tex]

so tension in the thread will be 22.6 N

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