Question

A block with mass mA = 15.0 kg on a smooth horizontal surface is connected by a thin cord that passes over a pulley to a second block with mass mB = 5.5 kg which hangs vertically.

Part A: Determine the magnitude of the acceleration of the system.

Part B: If initially mA is at rest 1.250 m from the edge of the table, how long does it take to reach the edge of the table if the system is allowed to move freely?

Part C: If mB = 1.0 kg, how large must mA be if the acceleration of the system is to be kept at g100?

--Express your answer to two significant figures and include the appropriate units.

Answer 1

By applying Newtons 2nd law

For Ma, Fnet =Ma*a

T=Ma*a------1

For Mb, Mb*g-T=Mb*a ------2

add equations 1 and 2,

Mb*g =(Ma+Mb)*a

a =(5.5 kg*9.80 m/s^2)/(15 kg+5.5 kg)

a =2.6 m/s^2

B)

From kinematic equation

x =vo*t+1/2*a*t^2

with vo=0 m/s

t =sqrt((2*x)/(a)) =sqrt((2*1.250 m)/(2.629268 m/s^2))

t =0.98 s

C)

From part A, a =(Mb*g)/(Ma+Mb) =g/100

Mb/(Ma+Mb) =1/100

Ma=99*Mb =99 kg