Answer to Question #252814 in Mechanics | Relativity for Kenzy

Question

A 200kg block is pushed along a horizontal frictionless table a distance of 3meter,by a horizontal force of 12newton. Find
i)how much work is done by the force
ii)the final kinetic energy of the block
iii)the final velocity
iv)Using newton's second law,find the acceleration and then the final velocity

Answer 1

i)

$W=Fd=12\cdot3=36$ J

F - horizontal force, d - distance

ii)

kinetic energy:

$E=W=36$ J

iii)

$E=mv^2/2$

$v=\sqrt{2E/m}=\sqrt{2\cdot36/200}=0.6$ m/s

iv)

$ma=F$

$a=F/m=12/200=0.06$ m/s²

$v=at+v_0$

$d=at^2/2+v_0t+d_0$

if start velocity $v_0=0$ and start distance $d_0=0$ , then:

$t=\sqrt{2d/a}$

final velocity:

$v=a\sqrt{2d/a}=0.06\sqrt{2\cdot3/0.06}=0.6$ m/s