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algol [13]
3 years ago
13

Let the masses of blocks A and B be 4.50 kg and 2.00 kg , respectively, the moment of inertia of the wheel about its axis be 0.4

00 kg⋅m2, and the radius of the wheel be 0.100 m . Find the magnitude of linear acceleration of block A if there is no slipping between the cord and the surface of the wheel.A. A of Block A
B. A of Block B
C. Alpha of pulley
D. Tension side A
E. Tension Side B

Physics
1 answer:
Free_Kalibri [48]3 years ago
7 0

Answer:

Accelerations of both the sides is 0.6125 m/s^{2}, A moves downwards whereas B moves upwards.

\alpha=6.125 rad/s^{2}

Tension on side A = 4.5 × g= 44.1 m/s^{2}

Tension on side B= 2.0 × g=  19.6 m/s^{2}

Explanation:

As both, the blocks A and B are attached due to the constraint they can only possess a single acceleration a.

Observe the figure attached, let the tension with Block A be T_{2} and the tension attached with Block B be T_{1} .

Tensions will be only be due to the weight of the blocks as no other force is present.

T_{2} = 4.5 × g= 44.1 m/s^{2}

T_{1} = 2.0 × g=  19.6 m/s^{2}

Now, lets make a torque equation about the center of the wheel and find the alpha

T_{2}×R- T_{1}×R= MI( Moment of Inertia of Wheel)× Alpha

where, R= Radius of the wheel=0.100m  and

           Alpha(\alpha)= Angular acceleration of the wheel

MI of the wheel= 0.400 kg/m^{2}

(44.1-19.6)R=0.400\alpha

\alpha = \frac{24.5 * 0.100}{0.400}

\alpha=6.125 rad/s^{2}

Acceleration = R ×\alpha

                    = 0.1 * 6.125

                    =0.6125 m/s^{2}

Accelerations of both the sides is 0.6125 m/s^{2}, A moves downwards whereas B moves upwards.

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equating all the forces acting  in x direction

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equating all the forces acting  in y direction

F sinθ + N -mg =0

now,

N = mg - F sinθ

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F cosθ = μ mg -μ F sinθ

F (cosθ + μsinθ ) = μ mg

F = \dfrac{\mu mg}{cos\theta + \mu sin\theta}

F = \dfrac{0.32 \times 22.2 \times 9.8}{cos 27.5^0+0.32 \times sin27.5^0}

F =67.28 N

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x = x0 + v0 t + 1/2 a t²

where

x: position at time t

v0: initial speed

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When the speed is constant (as before applying the brake), the equation would be:

x = x0 + v t

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b) After applying the brake, the car has an acceleration of -7.0 m/s². Using the equation for velocity, we can calculate how much time it takes the car to stop (v = 0):

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PE=mgh

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