Grade 11Mechanics
a ring of mass m and radius r has three particles attached to the ring as shown. the center of the ring has a speed V0. the kinetic energy of the system is : (slipping is absent)
4 Answers
vikas askiitian expert
velocity of left side particle is 21/2Vo
velocity of right side particle is 21/2Vo
velocity os particle at top is 2Vo
KE of ring = 1/2( Iw2+ mVo2) = 1/2(2mVo2)
KE of particles = 1/2(2M2Vo2+M(2Vo)2+M2Vo2) = 1/2(10MVo2)
total KE = 1/2(2mVo2+ 10MVo2) = Vo2(m+5M)
Rakesh kumar
velocity of left side particle is 21/2Vovelocity of right side particle is 21/2Vovelocity os particle at top is 2VoKE of ring = 1/2( Iw2+ mVo2) = 1/2(2mVo2)KE of particles = 1/2(2M2Vo2+M(2Vo)2+M2Vo2) = 1/2(10MVo2)total KE = 1/2(2mVo2+ 10MVo2) = Vo2(m+5M)
Manish
Kinetic energy of 3 particles +kinetic energy of ring
(1/2mv2+1/2mr2w2)+(1/2*2m*v2+1/2mr2w2)+1/2*m(v+v)2+1/2mr2w2)+(1/2mv2+1/2mr2w2)
=5mv2+mv2
=6mv2
Rishi Sharma
Dear Student,
Please find below the solution to your problem.
Since slipping is absent vo = Rωo
Speed of the 2m particle : square root (vo2+Rωo2)
= vo*square root (2)
Speed of the m(right) particle : square root(vo2+Rωo2)
= vo*square root(2)
Speed of the m(top) particle : vo+Rωo = 2vo
KE(total) = sum of individual KE
KE = 0.5*mvo^2 + 0.5*(mR^2)(Rvo)^2 + 0.5*(3m)(2vo)^2 + 0.5*(m)(2vo)^2
= 6mvo^2
∴x=6
Thanks and Regards
Please find below the solution to your problem.
Since slipping is absent vo = Rωo
Speed of the 2m particle : square root (vo2+Rωo2)
= vo*square root (2)
Speed of the m(right) particle : square root(vo2+Rωo2)
= vo*square root(2)
Speed of the m(top) particle : vo+Rωo = 2vo
KE(total) = sum of individual KE
KE = 0.5*mvo^2 + 0.5*(mR^2)(Rvo)^2 + 0.5*(3m)(2vo)^2 + 0.5*(m)(2vo)^2
= 6mvo^2
∴x=6
Thanks and Regards
Other Related Questions on mechanics
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
mechanics
Last Activity: 9 Months ago
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
mechanics
Last Activity: 9 Months ago
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat the free end, where a small mass of 2 g is positioned. determine(i) The velocity of the end when passing through the zero position(ii) The acceleration at maximum displacement(iii) The maximum kinetic energy of the mass
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass
mechanics
Last Activity: 3 Years ago
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
mechanics
Last Activity: 3 Years ago