How Do You Calculate the Acceleration of an Object Using Newton's Laws?

[zeshkani]

hi there i have a question in which i can't get the answer i will show my work on what i did, if anybody can help , that would help a lot .

here is the question:

only two forces act on an object (mass= 3kg)


x=40N
a=60N is at 45 degrees above the horizon
y= ?
find the magnitude and direction (relative to the x-axis) of the acceleration of the object?

i can use (a=60N)sin(45)= 42.42degrees, but where do i go from here, or what's the next step, i did try squaring y+x under the square root, but that's not the magnitude, because the answer in the back of the book is different.

any help is welcome thanks

 

[FunkyDwarf]

Ok first of all the 42.42 value won't be in degrees, it will be in Newtons. Secondly, draw a diagram, it always helps.

In order to help you more i need to know which direction the x force is in. so draw up what you think is happeneing and then attach it.

In essence you are just resolving vector components of a force, and need to draw a few triangles and stuff to find the resultant

 

[andrevdh]

Newton's second law can be applied in component form:

$$\Sigma F_x = ma_x$$

that is

$$a_x = \frac{\Sigma F_x}{m}$$

so to get the acceleration in the x-direction you need to add the force components acting on the object in the x-direction and divide that by its mass.