Question

a particle is pulled along a curved surface very slowly the coefficient of kinetic friction between the particle and the surface area is 0.4 the heat generated during the pulling of particle from lowest point a to the topmost point b is equal to(the mass of a particle equal to 5g)​

Answer 1

Answer:

S.A=0.4

m=5g

h=10m

Explanation:

thn the particles move upwards by the source of heat generation of the particles

Answer 2

given info : a particle is pulled along a curved surface very slowly the coefficient of kinetic friction between the particle and the surface area is 0.4.

To find : the heat generated during the pulling of particle from lowest point a to the topmost point b is equal to(the mass of a particle equal to 5g)...

solution : let an instant, particle makes an angle θ with horizontal.

friction force, fk = μN

now work done by the friction, Wf = ∫fk.ds cos180° [ here angle between frictional force and displacement is 180° because both are in opposite directions ]

= -∫μN ds

N = normal reaction of particle at that instant = mgcosθ

now, Wf = -∫μmgcosθ ds

= -μmg∫dscosθ

here dscosθ = dx

so, Wf = -μmg∫dx = -μmgx

from work energy theorem,

work done by force + Workdone by gravity + workdone by friction = kinetic energy

as particle is slowly pulled along the surface so, kinetic energy, ∆K = 0

work done by gravity = -mgy

so, work done by force - μmgx - mgy = 0

⇒work done by force = mg(μx + y)

here m = 0.005kg , g = 10 m/s² , μ = 0.4, x = 5 m and y = 10m

so, work dome, W = 0.005 × 10(0.4 × 5 + 10)

= 0.05 × (12)

= 0.6 J

therefore heat generated during the pulling of particle is 0.6 J