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An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= < 1 N , -1 N># and the second is #F_2 = < 5 N, 2 N>#. What is the object's rate and direction of acceleration?

Answer 1

Charlotte Aaron

The rate of acceleration is #=1.2ms^-2# in the direction #=9.5#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <1,-1>+<5,2>#

#=<6,1>#

We apply Newton's second Law

#vecF=m veca#

#veca =1/m*vecF#

#=1/5<6,1> = <6/5, 1/5>#

The magnitude of the acceleration is

#||veca||=||<6/5,1/5>||#

#=sqrt((6/5)^2+(1/5)^2)#

#=sqrt(37)/5=1.22ms^-2#

The direction is #theta = arctan((1/5)/(6/5))#

The angle is in the 1st quadrant

#theta=arctan(1/6)= 9.5#º

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Answer 2

Layla Ahmed

To find the object's acceleration, calculate the net force by summing the individual forces. Then, divide the net force by the mass of the object to find the acceleration vector. Net force = F₁ + F₂ = <1 N + 5 N, -1 N + 2 N> = <6 N, 1 N> Acceleration = Net force / mass = <6 N / 5 kg, 1 N / 5 kg> = <1.2 m/s², 0.2 m/s²> The rate of acceleration is 1.2 m/s², and the direction is along the x-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 #5 kg# is acted on by two forces. The first is #F_1= &lt; 1 N , -1 N&gt;# and the second is #F_2 = &lt; 5 N, 2 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= < 1 N , -1 N># and the second is #F_2 = < 5 N, 2 N>#. What is the object's rate and direction of acceleration?