Question 511: Electrostats & Capacitance

Question

An inclined plane making an angle of 30$$^\circ$$ with the horizontal is placed in a uniform horizontal electric field $$200{N \over C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.[g = 9.8 m/s2; $$\sin 30^\circ  = {1 \over 2}$$; $$\cos 30^\circ  = {{\sqrt 3 } \over 2}$$]

Accepted Answer

f = mg sin$$	heta$$ $$-$$ ($$\mu$$N + qE cos$$	heta$$)
F = mg sin$$	heta$$ $$-$$ $$\mu$$(mg cos$$	heta$$ + qE sin$$	heta$$) $$-$$ qE cos$$	heta$$
F = 1 $$	imes$$ 10 $$	imes$$ sin30
$$-$$ 0.2 (1 $$	imes$$ 10 $$	imes$$ cos30$$^\circ$$ + 200 $$	imes$$ 5 $$	imes$$ 10
$$-$$3
sin30$$^\circ$$)
$$-$$ 200 $$	imes$$ 5 $$	imes$$ 10
$$-$$3
cos30$$^\circ$$
$$ \Rightarrow $$ F = 2.3 N
$$a = {F \over m} = {{2.3} \over 1} = 2.3$$ m/sec
2
$$t = \sqrt {{{25} \over 9}}  = \sqrt {{{2 	imes 2} \over {2.3}}}  = 1.3$$ sec

Answer

0.46 s

Answer

0.92 s

Answer

1.3 s

Answer

2.3 s

Electrostats & Capacitance

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