An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < -2 N , -3 N># and the second is #F_2 = < 7 N, 1 N>#. What is the object's rate and direction of acceleration?

Answer 1

The resultant force acting is #<5,-2>#. The magnitude of the force is #5.4# #N#, leading to an acceleration of #1.8# #ms^-2# in a direction #21^o# below the positive x axis.

#F_1+F_2= <-2+7,-3+1> = <5,-2>#

#F=sqrt(5^2+(-2)^2)=sqrt(25+4)~~5.4# #N#

#a=F/m=5.4/3=1.8# #ms^-2#

#tan^-1((opp)/(adj))=tan^-1(-2/5)=-21^o#

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Answer 2

Xavier Adame

To find the object's acceleration, first calculate the net force acting on it by adding the individual forces. Then, use Newton's second law (F = ma) to find the acceleration vector. Net force = F_1 + F_2 = <-2 N + 7 N, -3 N + 1 N> = <5 N, -2 N> Using Newton's second law, F = ma, where F is the net force and m is the mass of the object (3 kg), solve for acceleration (a): a = F / m = <5 N / 3 kg, -2 N / 3 kg> = <1.67 m/s^2, -0.67 m/s^2> Therefore, the object's rate of acceleration is approximately 1.67 m/s^2 in the direction of the x-axis and -0.67 m/s^2 in the direction of the y-axis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= &lt; -2 N , -3 N&gt;# and the second is #F_2 = &lt; 7 N, 1 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < -2 N , -3 N># and the second is #F_2 = < 7 N, 1 N>#. What is the object's rate and direction of acceleration?