# Two forces acting on an object given in vectors - SOLVED

• runningphysics
In summary, vectors are mathematical quantities that have both magnitude and direction. To solve for the resultant of two forces given in vectors, you can use the head-to-tail method. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. Two forces can be in the same direction, and vectors can be represented graphically using arrows or line segments.
runningphysics
Homework Statement
Two forces act on a 3.4 kg mass and undergoes an acceleration a= .87i - .32j m/s^2. One force is F= -.7i - 3.0j N. What is the other in terms of i + j?
Relevant Equations
F=ma, F1 + F2= ma
I tried splitting the forces up into F1 and F2 making Newtons second law equation into F1+F2=ma. Then I added over the the first force given. multiply the mass to the acceleration terms to get F2= (m*ai + m*aj) - F1

Have you tried to look at it as components I and J as:

##F1_i + F2_i = m a_i## and similarly for j

## 1. What are vectors and how are they used in two forces acting on an object?

Vectors are mathematical quantities that have both magnitude and direction. In the context of two forces acting on an object, vectors are used to represent the magnitude and direction of each force. This allows us to accurately calculate the net force on the object.

## 2. How do you solve for the net force when given two forces acting on an object in vectors?

To solve for the net force, you must first find the components of each force in the x and y directions. Then, add the x components and the y components separately to find the total force in each direction. Finally, use the Pythagorean theorem to find the magnitude of the net force and use trigonometry to find its direction.

## 3. Can two forces acting on an object in vectors ever cancel each other out?

Yes, it is possible for two forces acting on an object in vectors to cancel each other out. This occurs when the two forces have equal magnitudes but are acting in opposite directions. In this case, the net force on the object would be zero and the object would remain at rest or continue moving at a constant velocity.

## 4. How does the angle between two forces affect the net force on an object?

The angle between two forces affects the net force on an object by changing the direction and magnitude of the net force. When the two forces are acting in the same direction, the net force will be larger than either individual force. When the two forces are acting in opposite directions, the net force will be smaller than either individual force. The angle between the two forces also determines the direction of the net force.

## 5. How can you use the principles of vectors to determine the acceleration of an object with two forces acting on it?

To determine the acceleration of an object with two forces acting on it, you must first find the net force on the object using vector addition. Then, use Newton's second law of motion (F=ma) to calculate the acceleration. The direction of the acceleration will be the same as the direction of the net force, and the magnitude of the acceleration will be determined by the mass of the object and the magnitude of the net force.

• Introductory Physics Homework Help
Replies
5
Views
3K
• Mechanics
Replies
21
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
984
• Introductory Physics Homework Help
Replies
5
Views
460
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
16
Views
1K
• Introductory Physics Homework Help
Replies
44
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
1K