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Mechanics

Hi can anyone give me some help on this question i'm not sure where to start

A particle, of mass 8kg, is attached to one end of a length of elastic string. The particle is placed on a smooth horizontal surface. The other end of the elastic string is attached to a point O fixed on the horizontal surface.

The elastic string had natural length 1.2m and modulus of elasticity 192N.

The particle is set in motion on the horizontal surface so that it moves in a circle, centre O, with a constant speed 3m/s.

Find the radius of the circle.

any help please?

i've ended up with a quadratic which i solved and selected the positive solution
my final answer for the radius is 1.5m can anyone confirm?

(edited 13 years ago)

Reply 1

jonathan3909

Use

F= \dfrac{mv^{2}}{r}

(edited 13 years ago)

Reply 2

hey_its_nay

Original post by jonathan3909

Use

F= \dfrac{mv^{2}}{r}

is v revolutions per minute? how do i convert it?
also is F the centripetal force?

Reply 3

jonathan3909

Original post by hey_its_nay

is v revolutions per minute? how do i convert it?
also is F the centripetal force?

F is the centripetal force (tension in the string) , v is the constant speed and m is the mass.

Reply 4

hey_its_nay

Original post by jonathan3909

F is the centripetal force (tension in the string) , v is the constant speed and m is the mass.

and the tension in the sting also equals ?x/l
?=192, l=1.2 but is x(the extention) r-l?

(edited 13 years ago)

Reply 5

jonathan3909

Original post by hey_its_nay

and the tension isn the sting also equals ?x/l
?=192, l=1.2 but is x(the extention) r-l?

Modulus of elasticity has no use here.The centripetal forces is the tension = 80N.

Reply 6

hey_its_nay

Original post by jonathan3909

Modulus of elasticity has no use here.The centripetal forces is the tension = 80N.

can you show me how you found the tension please?

(edited 13 years ago)

Reply 7

jonathan3909

Original post by hey_its_nay

and the tension in the sting also equals ?x/l
?=192, l=1.2 but is x(the extention) r-l?

Moreover in these types of questions , the length of the string is taken as the radius and since it is attached to a fixed point , the answer must be 1.2m!(think of it for yourself :rolleyes:

)

Reply 8

jonathan3909

Original post by hey_its_nay

can you show me how you the tension please?

Tension = mg
= (9.81 x 8)
= 78.48N ~ 79N

Reply 9

hey_its_nay

Original post by jonathan3909

Moreover in these types of questions , the length of the string is taken as the radius and since it is attached to a fixed point , the answer must be 1.2m!(think of it for yourself :rolleyes:

)