Question

A block of mass m1 = 3.7 kg on a frictionless plane inclined at angle =30o is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.3 kg. What are (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration of the hanging block, and (c) the tension in the cord?

Answer 1

a) 0.74m/s^2

b) going down

c) 21N

Step-by-step explanation:

To have a better understanding of this problem is necessary to draw a free body diagram.

Analysing the m1 box:

`-m1g*sin(\theta)+t1=m1*a`

and for m2:

`-m2*g+t2=m2*a`

`t2=-m2*a+m2*g`

the acceleration is negative because we assume is going downward

because the tension is the same we can substitude one formula into the other.

`-m1*g*sin(\theta)-m2*a+m2*g=m1*a`

`a=(2.3*9.8-3.7*9.8*sin(30))/(6.0)\\a=0.74m/s^2`

because the acceleration is positive the assumption was right.

The m1 block is going up and the m2 block is going down.

if we take a look of the m2 box:

`-mg+T=-m*a\\T=m(g-a)\\T=2.3(9.8-0.74)\\T=21N`