Question

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a massless string to a hook where M2 can be increased smoothly. The pulley has a negligible mass & no friction. When M2= 3.266 kg it begins to accelerate downward at a rate of 2.110 m/s2. Calculate u_s - u_k between M1 and the surface.

Answer 1

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a massless string to a hook where M2 can be increased smoothly. The pulley has a negligible mass & no friction. When M2= 3.266 kg it begins to accelerate downward at a rate of 2.110 m/s2. Calculate us - uk between M1 and the surface.

Here,

Force diagram for mass 2
T directed upward (tension of string)
M2g directed downward (force due to gravity on mass 2)

as Fnet = mass*acceleration

M2a = M2g - T
T = M2(g - a)
T = 3.266 (9.8 - 2.110)

T = 25.11 N

Force diagram for mass 1 , T directed right ,Ff directed left (force of friction)

M1a = T - Ff

6.330 = 25.11 -Ff

Ff = 25.11 - 6.330
Ff = 18.78 N

N directed upward (normal force of table) ,M1g directed downward (force due to gravity on mass 1)
No net force vertically

N = M1g ------------------------------------(3)

N = 6.330 *9.8
N = 62.034

as ,

(mu) = Ff/N ------------------------------------(4)

= 18.78 / 62.034

= 0.302

(mu) is the coefficient of friction which is 0.302

if the body is stationary this is coefficient of static friction and if the body is sliding this is coefficient of kinetic friction.

The coefficient of static friction is found by finding the minimum force required to get the system moving. In this case, when

T =(2.110)(9.81) = 20.69

coefficient of static friction is 20.69

(mu) is generally less than 1, although if a surface is very rough it can get to be 4,5 or higher. the smoother the surface the smaller (mu) is. The static (mu) is generally greater than the kinetic (mu)