Question

An object with a mass M = 250 g is on a plane inclined at 30º above the horizontal and is attached by a string to a mass m = 150 g. There is no friction and mass m hangs freely and is initially at rest. When mass m has descended a distance h = 10 cm, its speed will be?

Answer 1

0.495 m/s

Step-by-step explanation:

`T` = tension force in the string connecting the two objects

`M` = Mass of the object on inclined plane = 250 g = 0.250 kg

`m` = Mass of the hanging object = 150 g = 0.150 kg

`a` = acceleration of each object

From the force diagram, force equation for the motion of the object on the inclined plane is given as

`T - Mg Sin30 = Ma\\T = Mg Sin30 + Ma`

From the force diagram, force equation for the motion of the hanging object on the inclined plane is given as

`mg - T = ma\\T = mg - ma`

Using the above two equations

`Mg Sin30 + Ma = mg - ma`

`(0.250)(9.8) Sin30 + (0.250) a = (0.150) (9.8) - (0.150)a`

`a = 0.6125 ms^(-2)`

`h` = height dropped by the hanging object = 10 cm = 0.10 m

`v` = Speed gained by the object

Speed gained by the object can be given as

`v = sqrt(2ah)\\v = sqrt(2(0.6125)(0.20))\\v = 0.495 ms^(-1)`