Question
A $$10\,kg$$ block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius $$10\,m.$$ The applied force is of $$200\,N$$ as shown in figure. If the block had started from rest at $$A,$$ the velocity at $$B$$ would be
A $$10\,kg$$ block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius $$10\,m.$$ The applied force is of $$200\,N$$ as shown in figure. If the block had started from rest at $$A,$$ the velocity at $$B$$ would be
A.
$$1.7\,m/s$$
B.
$$17\,m/s$$
C.
$$27\,m/s$$
D.
$$34\,m/s$$
Answer :
$$17\,m/s$$
Solution :
$$\eqalign{ & {W_{{\text{gravity }}}} + {W_F} = \Delta K - 10 \times g\left( {10 - 10\cos {{60}^ \circ }} \right) + 200 \times 10\sin {60^ \circ } \cr & = \frac{1}{2} \times 10 \times v_f^2 - 0 \cr & \therefore {v_f} = 17\,m/s \cr} $$
$$\eqalign{ & {W_{{\text{gravity }}}} + {W_F} = \Delta K - 10 \times g\left( {10 - 10\cos {{60}^ \circ }} \right) + 200 \times 10\sin {60^ \circ } \cr & = \frac{1}{2} \times 10 \times v_f^2 - 0 \cr & \therefore {v_f} = 17\,m/s \cr} $$