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given answer may be wrong. The two blocks A and B are connected by a light strin

ID: 1972059 • Letter: G

Question

given answer may be wrong.

The two blocks A and B are connected by a light string that passes over a frictionless pulleys, as shown below. The mass of block A is 10.0 kg, and the mass of blocks B is 25.0 kg. The coefficient of friction between block and incline surface is 0.08. Draw free-body force diagram of block A and block B. Create the force table for block A and block B based on your reference flame. Write down the Newton's component equations for A and B. Find the acceleration of block A and the tension force of the string.

Explanation / Answer

1) The forces acting on A : T,mgsin45,N,mgcos45; [m = mass of A ]

T-tension in the rope,

mgsin45 is component of its weight acting downwards along the incline,

mgcos45 is component of its weight acting downward along the normal direction to the plane,

N is normal reaction at the surface contact of A and the incline acting upwards on A and normal to the plane.

The forces acting on B : T,Mg [M - mass of B]

T - tension in the rope acting upward along the rope

Mg - weight acting along downward direction on B

2) & 3) Net forces acting on A :

N = mgcos45 ; T = mgsin45

Net forces acting on B :

T = Mg ;

The above equations are for static equilibrium of the system

4) In motion, an extra force f(kinetic friction) comes into the picture and this acts opposite to the motion of a block along its contact surface

Let A is going upwards along the incline and B is moving downward .

The equation of motions are :

for A :

T - mgsin45 - f = ma ;

f = N ; [-coefficient of friction]

N = mgcos45 = mg/2 ;

=> T -  N - mg/2 = ma ;

=> T - 0.08(mg/2) -mg/2 = ma ;

=> T -7.637g = 10a ; -----------------------------------(i)

for B :

Mg - T = Ma ; ------------------------------------------(ii)

adding (i),(ii)

=> Mg - 7.637g = 35a

=> a = 4.86 m/s2   [g = 9.8m/s2]

and T = M(g-a) from (ii)

=> T = 25(9.8-4.86) = 123.5 N