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An object with a mass M= 250 g is on a plane inclined at 30 degreesabove the horizontal and is attached by a string to a mass m = 150g. There is no friction and mass m hangs freely and isinitially at rest. When mass m has descended a distance h = 10 cm,its speed will be
(a) 35.0 cm/s
(b) 7.0 cm/s
(c) 140 cm/s
(d) 110cm/s
(e) 70.0 cm/s

Respuesta :

Answer:

a) v = 35 cm/s

Explanation:

Here the work done by gravity on two masses is equal to the change in kinetic energy of the two masses

so here in m = 150 g mass moves down then other mass M = 250 g will move up by same distance on inclined plane

so we have

[tex]mgd - Mgsin\theta d= \frac{1}{2}mv^2 + \frac{1}{2}Mv^2[/tex]

here we know that

[tex]m = 150g[/tex]

[tex]M = 250 g[/tex]

[tex]\theta = 30 degree[/tex]

[tex]d = 10 cm = 0.10m[/tex]

so we will have

[tex](0.150)9.81\times 0.10 - (0.250)9.81sin30\times 0.10 = (\frac{1}{2}(0.150) + \frac{1}{2}(0.250))v^2[/tex]

[tex]0.0245 = 0.2 v^2[/tex]

[tex]v = 0.35 m/s[/tex]

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