An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 8 N , -4 N># and the second is #F_2 = < 2 N, 6 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2018-03-17T06:53:55

The rate of acceleration is #=2.55ms^-2# in the direction #=11.3^@# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF= <8,-4> + <2,6> = <8+2, -4+6> #

# = <10,2> N#

The mass of the object is #m=4kg#

According to Newto's Second Law

#vecF=mxx veca#

Therefore,

#veca=1/m*vecF= 1/4* <10,2> = <10/4, 2/4> #

#= <5/2,1/2> ms^-2#

The rate of acceleration is

#||veca|| = || <5/2,1/2> || = sqrt ((5/2)^2+(1/2)^2) #

#=sqrt(25/4+1/4)= sqrt26/2=2.55ms^-2#

The direction is

#theta=arctan((1/2)/(5/2)) = arctan(0.2)=11.3^@# anticlockwise from the x-axis