Question

1) A block of mass m1 is moving at a constant speed in a circle on the frictionless surface of a large table. It is connected to another mass m2 by a light inextensible string of length d that passes through a hole in the surface of the table. Exactly half of the string is below the table and half is above.

A) Give an expression for the centripetal force acting on m1 in terms of given quantities

B) Provide an expression for the speed v of m1 in tersm of given quantities and constant terms. AND C) calculate v if m1 = 5 kg, m2 = 2.5 kg, and d = 0.3m

Answer 1

Part-a

The weight of the hanging mass, m2, provides the centripetal force that the spinning
mass, m1, needs to keep it from sliding o the table due to its inertia.

therefore

Cetripetal force is given by

(r is the radius of the circle )

Hence

this is the required expression for centripetal force.

Part-b

We know that

we get

Part-c

m₁=5 kg , m₂ = 2.5 kg and d=r=0.3m

BY plugging these values in the expression of velocity we get

which gives us

Hence the velocity of the block m₁ is 1.21 m/s