Given : The sphere, which is a rest, of mass m is attached by a wire and a strin

Question

Given:

The sphere, which is a rest, of mass m is attached by a wire and a string as shown in the figure. The length of the wire is L. Initially, the wire makes an angle of theta to the vertical. Assume that the ratio of the sphere radius to the wire length L is very small, and also assume that the terms m, theta, and L are known.

Find:

a) The free body diagram (FBD) of the sphere as shown.

b) The tension in the wire as shown.

c) The free body diagram (FBD) of the sphere AFTER THE STRING IS CUT.

d) The tension in the wire AFTER THE STRING IS CUT.

Explanation / Answer

a) FBD of sphere is tension T along the wire , weight of the sphere (mg)downwards and the force due to the string towards left.

b) Equating vertical components of force the component Tcos(theta) is actind upwards which balance weight therefore Tcos(theta)=mg ===> T=mg/cos(theta)

Tsin(theta)= T1(tension in the string) ==>T1 = mgtan(theta)

c)after sting is cut the tension remains same and the leftward force is absent

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