A solid sphere of mass 2, kg is resting insid | vedclass

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Question

(C) Given velocity of the cube: $\vec v = 5t\,\hat i + 2t\,\hat j$.Acceleration of the cube: $\vec a = \frac{d\vec v}{dt} = 5\,\hat i + 2\,\hat j\,m/s

Vedclass · Accepted Answer

$26\,N$

Vedclass · Answer

(C) Given velocity of the cube: $\vec v = 5t\,\hat i + 2t\,\hat j$.Acceleration of the cube: $\vec a = \frac{d\vec v}{dt} = 5\,\hat i + 2\,\hat j\,m/s^2$.Here,$a_x = 5\,m/s^2$ and $a_y = 2\,m/s^2$.In the frame of the cube,the sphere experiences a pseudo force $\vec F_p = -m\vec a = -m(5\,\hat i + 2\,\hat j)$.The forces acting on the sphere in the cube's frame are:$1$. Weight: $\vec W = -mg\,\hat j = -2(10)\,\hat j = -20\,\hat j\,N$.$2$. Pseudo force: $\vec F_p = -2(5\,\hat i + 2\,\hat j) = -10\,\hat i - 4\,\hat j\,N$.$3$. Normal forces from the walls of the cube: $\vec N_x$ (from wall $AD$) and $\vec N_y$ (from wall $DC$).Since the sphere is at rest relative to the cube,the net force is zero:$\vec N_x + \vec N_y + \vec W + \vec F_p = 0$.$\vec N_x = -(-10\,\hat i) = 10\,\hat i\,N$.$\vec N_y = -(-20\,\hat j - 4\,\hat j) = 24\,\hat j\,N$.The total force exerted by the sphere on the cube is the vector sum of the normal forces: $\vec N = \vec N_x + \vec N_y = 10\,\hat i + 24\,\hat j\,N$.The magnitude is $N = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26\,N$.

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