Question
A straight bar, of mass $$15\,kg$$ and length $$2\,m,$$ at rest on a frictionless horizontal surface, receives an instantaneous impulse of $$7.5\,Ns$$ perpendicular to the bar. If the impulse is applied at the mid point of the bar, the energy transfered is
A straight bar, of mass $$15\,kg$$ and length $$2\,m,$$ at rest on a frictionless horizontal surface, receives an instantaneous impulse of $$7.5\,Ns$$ perpendicular to the bar. If the impulse is applied at the mid point of the bar, the energy transfered is
A.
$$3.2\,J$$
B.
$$1.9\,J$$
C.
$$3.8\,J$$
D.
$$2.5\,J$$
Answer :
$$1.9\,J$$
Solution :
$$\eqalign{ & J = m\left( {{v_f} - {v_i}} \right)\,\,{\text{or}}\,\,7.5 = 15\left( {{v_f} - 0} \right) \cr & \Rightarrow {v_f} = 0.5\,m/s \cr & \therefore K = \frac{1}{2}m{v^2} = \frac{1}{2} \times 15 \times {0.5^2} = 1.9\,J \cr} $$
$$\eqalign{ & J = m\left( {{v_f} - {v_i}} \right)\,\,{\text{or}}\,\,7.5 = 15\left( {{v_f} - 0} \right) \cr & \Rightarrow {v_f} = 0.5\,m/s \cr & \therefore K = \frac{1}{2}m{v^2} = \frac{1}{2} \times 15 \times {0.5^2} = 1.9\,J \cr} $$