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
A)35.0 cm/s
B)7.00 cm/s
C)140 cm/s
D)110 cm/s
E)70.0 cm/s

Question

Quizplus · Accepted Answer

Explanation:The potential energy of the system is converted into kinetic energy. The potential energy of the system is given by:$$U = Mgh + mgh$$where M is the mass of the object on the inclined plane, m is the mass of the hanging object, g is the acceleration due to gravity, and h is the distance the hanging object has descended.The kinetic energy of the system is given by:$$K = (M + m)v^2/2$$where v is the speed of the hanging object.By conservation of energy, we have:$$U = K$$$$Mgh + mgh = (M + m)v^2/2$$$$v = sqrt((2(M + m)gh)/(M + m))$$$$v = sqrt((2(0.25 kg + 0.15 kg)(9.8 m/s^2)(0.1 m))/(0.25 kg + 0.15 kg))$$$$v = 0.35 m/s = 35.0 cm/s$$

An Object with a Mass M = 250 G Is