Question 283: Work, Energy and Power & Circular Motion

Question

A block moving horizontally on a smooth surface with a speed of 40 ms
$$-$$1
splits into two equal parts. If one of the parts moves at 60 ms
$$-$$1
in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = ___________.

Accepted Answer

P
i
= P
f
m $$	imes$$ 40 = $${m \over 2}$$ $$	imes$$ v + $${m \over 2}$$ $$	imes$$ 60
40 = $${v \over 2}$$ + 30
$$\Rightarrow$$ v = 20
(K. E.)
I
= $${1 \over 2}$$m $$	imes$$ (40)
2
= 800 m
(K. E.)
f
= $${1 \over 2}$$$${m \over 2}$$ . (20)
2
+ $${1 \over 2}$$ . $${m \over 2}$$ (60)
2
= 1000 m
| $$\Delta$$ K. E. | = | 1000m $$-$$ 800 m | = 200 m
$${{\Delta K.E.} \over {{{(K.E.)}_i}}} = {{200m} \over {800m}} = {1 \over 4} = {x \over 4}$$
x = 1

Work, Energy and Power & Circular Motion

A block moving horizontally on a smooth surface with a speed of 40 ms $-1 splits into two equal parts. If one of the parts moves at 60 ms -$1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = ___________.

Integer / Numeric Answer Type