# Find the acceleration vector of the mass

• XwakeriderX
In summary: But that is only a shortcut to see what the components of the vector are.In summary, the problem involves finding the acceleration vector of a 10.0 kg mass under the influence of two forces, F1 and F2. After adding the two forces and dividing by the mass, the acceleration is found to be (0.6x-0.16y) m/s2. However, this answer is incorrect as the components of the acceleration vector must be divided by the square root of 10. A shortcut to finding the components is to divide them by the square root of 10 twice.
XwakeriderX

## Homework Statement

Two forces are acting on a 10.0 kg mass. The forces are:
F1 = (12.3 x - 13.5 y) Newtons where x and y are unit vectors
F2 = ( -6.30x + 11.9y) Newtons

A) Find the acceleration vector of the mass. Express your answer in unit vector
form.

F=MA

## The Attempt at a Solution

I added the two vectors getting
(6.0x-1.6y) Newtons then i divided it by the mass to get the acceleration

So my final answer is a= (0.6x-0.16y) m/s2

is this correct?

Last edited:

XwakeriderX said:
So my final answer is a= (0.6x-0.16y) m/s2

is this correct?

You divided each vector (x and y) by ten, meaning that the result was that you were dividing it by ten, twice, resulting in 100.

Ex: if your vector was 20x + 20y, that magnitude is 400, so dividing each component by 10,
2x + 2y, you get a magnitude of 4.

You need to find the magnitude of 6x - 1.6y (Pythagorean) and divide THAT by ten, then use trigonometry to find the x,y components at that magnitude.
Or, a shortcut is to divide each component by sqrt(10) since the sqrt(10) ^ 2 is 10, so by dividing by the sqrt(10) twice (once to each component) you are ultimately dividing by 10.

## 1. What is the definition of acceleration?

Acceleration is the rate at which an object's velocity changes over time. It can be calculated by dividing the change in velocity by the change in time.

## 2. How is acceleration related to force?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship can be expressed as a = F/m, where a is acceleration, F is force, and m is mass.

## 3. What is the difference between average acceleration and instantaneous acceleration?

Average acceleration is the average rate of change of velocity over a given time period, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated by dividing the change in velocity by the time interval, while instantaneous acceleration can be found by taking the derivative of the object's velocity function with respect to time.

## 4. How do you find the acceleration vector of a mass?

To find the acceleration vector of a mass, you can use the formula a = F/m, where a is acceleration, F is the net force acting on the mass, and m is the mass. The acceleration vector will have both magnitude and direction, and can be represented graphically as an arrow pointing in the direction of the acceleration.

## 5. What factors can affect the acceleration of a mass?

The acceleration of a mass can be affected by various factors including the net force acting on the mass, the mass of the object, and external factors such as friction and air resistance. In addition, the acceleration may also change if there is a change in the direction or magnitude of the force acting on the mass.

Replies
1
Views
823
Replies
23
Views
2K
Replies
17
Views
2K
Replies
44
Views
2K
Replies
5
Views
3K
Replies
2
Views
915
Replies
9
Views
1K
Replies
1
Views
2K
Replies
30
Views
2K
Replies
42
Views
4K