An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -6 N , 3 N># and the second is #F_2 = < 6 N, 5 N>#. What is the object's rate and direction of acceleration?

Answer 1

Isabella Alvarez

The acceleration is #2# #m/s^2# and the angle is #90^\circ#.

When you want to sum two vectors in classical mechanics, it is enough if you sum them component by component.

The final vector is

#F=F_1+F_2=<-6N+6N, 3N+5N>#

#=<0N, 8N>#

The length of a vector is given by

#L=sqrt(x^2+y^2)#

that of our vector is

#L=sqrt(0^2+8^2)=8#.

Then the force is with a magnitude of 8N and the acceleration is given by

#F=ma#

#a=F/m=8/4=2# #m/s^2#

The direction is given by

#\theta=arctan(y/x)=arctan(8/0)#

This of course is a problem because we cannot divide by zero. On the other hand we know that the arctan is singular when the angle is #pi/2#. So the direction is an angle of #pi/2# or #90^\circ#.

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Answer 2

Amelia Adams

To find the object's acceleration, first calculate the net force by adding the two forces together: F_net = F_1 + F_2 = <-6 N + 6 N, 3 N + 5 N> = <0 N, 8 N> Then, use Newton's second law, F = ma, to find the acceleration: a = F_net / m = <0 N / 4 kg, 8 N / 4 kg> = <0 m/s², 2 m/s²> So, the object's rate of acceleration is 2 m/s² in the direction of the positive 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 #4 kg# is acted on by two forces. The first is #F_1= &lt; -6 N , 3 N&gt;# and the second is #F_2 = &lt; 6 N, 5 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -6 N , 3 N># and the second is #F_2 = < 6 N, 5 N>#. What is the object's rate and direction of acceleration?