Q

A man of mass () is sitting in a train movingwith velocity  . He observe that a block of mass  is moving towards him with velocity . Then the kinetic energy of block w.r.t  man is (Assume )

S safeer

K.E of the block from the reference frame of the train is

$\frac{1}{2} m (v_1+ v_2) ^2$

$\\=\frac{1}{2} \times 5 \times [ 3+5] ^2 = 1/2 \times 5 \times 64\\ \\ =5 \times 32 = 160 J$

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in the figure. Work done by normal reaction on block in time t is:

S safeer

By balancing the forces in vertical direction, we get:

$\Rightarrow N-Mg=\frac{Mg}{2}\Rightarrow N=\frac{3mg}{2}$

and displacement is given by equation:

$s=ut+\frac{1}{2}at^2$

where u=0 and a=g/2

$\Rightarrow\vec{S}=\frac{1}{2}\vec{\frac{g}{2}}t^{2}$

and we know,

$W_{N}=\vec{N}.\vec{S}$

$\Rightarrow W=\frac{3mg^{2}t^2}{8}$

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