Dynimacs course please help me with this question ASAP Dynim

Dynimacs course please help me with this question ASAP Dynimcs course with the show work and please put square on the final answer

Part A The spool has a mass of 105 kg and a radius of gyration of kG = 0.3 If the coefficients of static and kinetic friction at A are 8 determine the angular acceleration of the spool if P - 49N. Solve this problem if the cord and force P- 49N are directed vertically upwards. (Figure 1) -0.2 and k 0.15, respectively, Express your answer with the appropriate units. Figure 1 of 1 =| Value Units Submit My Answers Give Up Provide FeedbacK Continue 250 mm 400 mm

Solution

Data Given

Mass of the spool = 105 kg

Radius of gyration Kg = 0.3m

Radius of spool(R) = 0.4m

Area of cross section of the spool = 3.14 x R^2 = 3.14 x 0.4^2 = 0.5 m^2

Moment of inertia (I) = m x Kg^2 = 105 x 0.3^2 = 9.45 kgm^2

P = 49N

Torque on the spool = P x R = 49 x 0.4 = 19.6 Nm

Torque(T) = Moment of inertia x angular accleration

19.6 = 9.45 x Angular acceleration

Angular acceleration = 19.6/9.45 = 2.07 m/s^2

Coefficient of static friction = 0.2

Coefficient of kinetic friction = 0.15

Frictional force in horizontal direction = 0.15 x P = 0.15 x 49 = 7.35 N

Effective force on the spool = 49 -7.35 = 41.65N

Torque on the spool = 41.65 x 0.4 = 16.7 Nm

T= MI x Angular acceleration

Angular acceleration = T/MI = 16.7/9.45 = 1.76 m/s^2

Force in vertically upwards direction = 49 N

Weight of the spool = 105 Kg

= 105 x 9.81 N = 1030N

Since the weight of the spool is more than the vertical force, the vertical force 49N will have no effect on the spool.