11.8 Example 8

A block A is above a block B, as show the image. Both blocks are in rest. If the block A have a mass of 1.7 kg, block B have 4 kg, and there isn’t friction, Which are the accelerations of the blocks when these leaves the rest? Which are the velocities after 0.2 seconds?

Solution with FisicaLab

Erase the content of the chalkboard and select the SI system. And add one element Stationary reference system, one element Block with horizontal movement, one element Block above an inclined plane to the left, and one element Relative motion. And add the necessary elements Force to make the free body diagram of each block. As show the image below:

To the element Stationary reference system, write:

g

9.81

t

0.2

To the element Block above an inclined plane to the left, the block A, write:

Name

A

m

1.7

ang

36

a

aA

vi

0

vf

vfA

d

dA

Relative to

B

Note that the movement of this block is relative to the block B. To its normal force:

f

nA

ang

54

To the element Block with horizontal movement, the block B, write:

Name

B

m

4

a

aB

vi

0

vf

vfB

d

dB

Relative to

sf

To its normal force:

f

nB

To the force applied to the block A:

f

nA

ang

54

The element Relative motion is necessary to get the acceleration, velocity and travelled distance of the block A, in reference to the stationary system. All these are unknown data, then write:

Object

A

asf

asfA

ang_asf

ang_asfA

vfsf

vfsfA

ang_vfsf

ang_vfsfA

dsf

dsfA

ang_dsf

ang_dsfA

Now click in the icon Solve to get the answer:

nA = 11.765 N ;  nB = 48.758 N ;  aA = -7.165 m/s2 ;
vfA = -1.433 m/s ;  dA = -0.143 m ;  aB = 1.729 m/s2 ;
vfB = 0.346 m/s ;  dB = 0.035 m ;  asfA = 5.855 m/s2 ;
ang_asfA = 225.994 degrees ;  vfsfA = 1.171 m/s ;
ang_vfsfA = 225.994 degrees ; dsfA = 0.117 m ;
ang_dsfA = 225.994 degrees ;
Status = success.