# Acceleration from 2 Force Vectors

• zcabral
In summary, the problem involves two forces, F1 and F2, acting on a 2.00 kg object at an angle of 60 degrees. The magnitude of the acceleration is found to be 17.67 using the formula a=sqrt(ax^2+ay^2). However, the direction of the acceleration is still incorrect. To solve this, the two forces should be combined into a single one and the calculation for Fy should be redone to get the correct value.
zcabral

## Homework Statement

Two forces, F1 and F2, act on a 2.00 kg object where F1 = 30.0 N (on the x-axis) and F2 = 10.0 N. A 60 degree angle is between them. Find the magnitude and direction of the acceleration.

http://www.webassign.net/pse/p5-15.gif (ignore figure a)

## Homework Equations

F=ma
a=sqrt. (ax^2 + ay^2)

## The Attempt at a Solution

I figured out that the magnitude is a=sqrt. (ax^2 + ay^2)
which is equal to 17.67

however i can't get the correct direction! i thought it would be theta = arctan (2.5 /17.5)= 8.13 but it keeps saying its not the right answer! help

Last edited:
The angle should be arctan (a_y/a_x).

General rules for these problems:

Use units throughout.
Combine the two forces into a single one.
Show all work.

i did that and it didnt come out right

zcabral said:
i thought it would be theta = arctan (2.5 /17.5)= 8.13 but it keeps saying its not the right answer! help
Where did you get the numbers 2.5 and 17.5? What are they?

2.5= ay
17.5= ax

together they are the acceleration = 17.67 (im 100% sure)

i got them by using this technique
Fx= 30cos(0)+10cos(60)= 35
A=F/m A= 35/2 A= 17.5

Fy= 30sin(0)+10cos(60)= 5
A=F/m A= 5/2 A= 2.5

zcabral said:
2.5= ay
17.5= ax

together they are the acceleration = 17.67 (im 100% sure)

i got them by using this technique
Fx= 30cos(0)+10cos(60)= 35
A=F/m A= 35/2 A= 17.5

Fy= 30sin(0)+10cos(60)= 5
A=F/m A= 5/2 A= 2.5

oops no i used sine just didnt type it out right here

zcabral said:
oops no i used sine just didnt type it out right here
But $10 \sin(60) \ne 5$

why is it the cos(0) and sin(0)

portillj said:
why is it the cos(0) and sin(0)
Because the angle that the 30 N force makes with the x-axis is 0. (That force is along the x-axis.)

how do i find out the angle is i have the magnitudes??

## What is "Acceleration from 2 Force Vectors"?

"Acceleration from 2 Force Vectors" is a concept in physics that describes the resulting acceleration of an object when two or more forces are acting on it simultaneously.

## How do you calculate the acceleration from 2 force vectors?

The acceleration from 2 force vectors can be calculated by dividing the net force acting on an object by its mass. This can be represented by the equation a = F/m, where a is the acceleration, F is the net force, and m is the mass of the object.

## What is the difference between acceleration from 2 force vectors and acceleration from a single force?

The main difference is that acceleration from 2 force vectors takes into account multiple forces acting on an object, while acceleration from a single force only considers one force. This means that acceleration from 2 force vectors is the result of the combined effect of multiple forces, while acceleration from a single force is the direct result of that single force.

## What are some real-life examples of acceleration from 2 force vectors?

One example is a car accelerating on a flat road. The car's engine provides a forward force, while friction from the road and air resistance provide opposing forces. The resulting acceleration is a combination of these forces. Another example is a rocket launching into space, where the thrust from the rocket engines and the force of gravity both contribute to the acceleration of the rocket.

## How does Newton's Second Law of Motion relate to acceleration from 2 force vectors?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that when there are two or more forces acting on an object, the resulting acceleration will be determined by the net force and the mass of the object, in accordance with this law.

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