Dynimacs course please help me with this question ASAP Dynimcs course with the s

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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

Explanation / Answer

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.

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