An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <-3 N , -5 N># and the second is #F_2 = < 6 N, 7 N>#. What is the object's rate and direction of acceleration?

Answer 1

Adding the vectors gives a magnitude of #3.6# #N#, and an angle of #34^o#.

Using Newton's Second Law:

#a=F/m=3.6/2=1.8# #ms^-2# at #34^o# to the positive x-axis.

First we find the resultant force acting on the object, by adding the components of the force vectors:

#F_1+F_2=<-3,-5>+<6,7># #=<(-3+6),(-5+7)> =<3,2>#
So the resultant force vector is 3 in the x direction and 2 in the y direction. We can use Pythagoras' theorem to find the magnitude of the resultant: #sqrt(3^2+2^2)=sqrt13~~3.6# #N#.

To find the direction, we use trig: 3 and 2 are the opposite and adjacent sides of a right-angled triangle, so:

#tan theta=(opp)/(adj)=2/3# so #theta ~~ 34^o#

Using Newton's Second Law, the acceleration is given by:

#a=F/m=3.6/2=1.8# #ms^-2# at #34^o# to the positive x-axis.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2
The net force is \( F_{\text{net}} = F_1 + F_2 = <3\ \text{N}, 2\ \text{N}> \). Using Newton's second law \( F_{\text{net}} = m \cdot a \), where \( m = 2\ \text{kg} \): \( a = \frac{F_{\text{net}}}{m} = <\frac{3}{2}\ \text{m/s}^2, 1\ \text{m/s}^2> \). Therefore, the object's rate of acceleration is \( <\frac{3}{2}\ \text{m/s}^2, 1\ \text{m/s}^2> \), and the direction is in the \( x \)-direction and \( y \)-direction, respectively.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7