Question

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

Answer 1

a) v = 35 cm/s

Step-by-step 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

`mgd - Mgsin\theta d= (1)/(2)mv^2 + (1)/(2)Mv^2`

here we know that

`m = 150g`

`M = 250 g`

`\theta = 30 degree`

`d = 10 cm = 0.10m`

so we will have

`(0.150)9.81* 0.10 - (0.250)9.81sin30* 0.10 = ((1)/(2)(0.150) + (1)/(2)(0.250))v^2`

`0.0245 = 0.2 v^2`

`v = 0.35 m/s`