# Find Magnitude & Direction for acceleration

In summary, the homework statement states that Block B has acceleration of 4 m/s2. Relative acceleration of block A with respect to Block B is 4 m/s2. Find the magnitude and direction of the acceleration for block A.

## Homework Statement

Block B has acceleration of 4 m/s2... Relative acceleration of block A w/ respect to B is 4 m/s2. Find magnitude & direction of accel for A?

## Homework Equations

a_A = a_B + a_A/B

x_A = x_B + x_A/B

y_A = y_B + y_A/B

## The Attempt at a Solution

x & y components:
-4cos(20) = -3.76
-4sin(20) = -1.37

-3.76 = 4 + x_A/B

x_A/B = -7.76

y_A/B = -1.37

|a| = sqrt( -7.76^2 + -1.37^2 ) = 7.88 m/s2

direction: tan -1 * (-1.37/-7.88) = 10.01 degrees

#### Attachments

• accel2.png
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aa|b :
x & y components:
-4cos(20) = -3.76
-4sin(20) = -1.37

aa = ab + aa|b
x components:
-3.76 = 4 + x_A/B

Check above.

Last edited by a moderator:
what is the next step to find the magnitude of acceleration for a_A, are you saying use (-3.76, -1.37) as the x&y components?

I just added an extra line to my post. Can you fix your line I've marked with a cross?

NascentOxygen said:
I just added an extra line to my post. Can you fix your line I've marked with a cross?

NascentOxygen said:

Check above.
I'm not sure what you mean by that? ...so are you saying for the x & y components I need to use are (-3.76, -1.37). How do you find the magnitude & direction for acceleration for this particular problem? please help, I need a clear response.

Last edited by a moderator:
Those are the x and y components of the smaller block's relative acceleration, yes. You worked them out.

I pointed out that you incorrectly applied the formula (which I highlighted by writing it in red). Can you apply that formula correctly to determine the x component of a's acceleration? So I'm saying there is something wrong in how you substituted values into that formula aa = ab + ...

NascentOxygen said:
Those are the x and y components of the smaller block's relative acceleration, yes. You worked them out.

I pointed out that you incorrectly applied the formula (which I highlighted by writing it in red). Can you apply that formula correctly to determine the x component of a's acceleration? So I'm saying there is something wrong in how you substituted values into that formula aa = ab + ...
so should it be something like ... a_A = (4*i + (- 3.76*j) ) + ( 0*i + (-1.37*j) ) = 0.24*i - 1.37*j

so should it be something like ... a_A = (4*i + (- 3.76*j) ) + ( 0*i + (-1.37*j) ) = 0.24*i - 1.37*j
You can do it that way if you wish. Next, you're asked to express as a magnitude and direction ...

NascentOxygen said:
You can do it that way if you wish. Next, you're asked to express as a magnitude and direction ...
Okay, for magnitude I did: |a| = sqrt ( (0.24^2) + (-1.37^2) = 1.39 m/s2

and direction I did inverse tangent of (y/x) which is ( -1.37 / 0.24 ) = - 80.06 deg ...which I'm not sure is right

Those look to be around what I was expecting.

You should be able to go back to your first post in this thread, and without doing any further calculations, sketch the triangle showing this vector relation: a_A = a_B + a_A/B

Hint: The first line in your first post tells you that the triangle will be isoscles.

I got the right answers, 1.39 & - 80.06, thanks for all ur help, highly appreciated

## 1. What is 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 do you find the magnitude of acceleration?

The magnitude of acceleration can be found by using the equation a = ∆v/∆t, where ∆v is the change in velocity and ∆t is the change in time. This will give you the numerical value of acceleration in units of distance per time squared (e.g. m/s^2).

## 3. What is the direction of acceleration?

The direction of acceleration can be determined by the direction of the change in velocity. If the velocity is increasing, the acceleration is in the same direction as the velocity. If the velocity is decreasing, the acceleration is in the opposite direction.

## 4. How do you calculate the direction of acceleration?

The direction of acceleration can be calculated using the equation tanθ = ∆vy/∆vx, where ∆vy is the change in vertical velocity and ∆vx is the change in horizontal velocity. This will give you the angle of acceleration from the horizontal axis.

## 5. How do I interpret the magnitude and direction of acceleration?

The magnitude of acceleration tells us how much an object's velocity is changing, while the direction tells us in which direction it is changing. For example, a large magnitude of acceleration in the direction of motion indicates that the object is speeding up, while a small magnitude of acceleration in the opposite direction indicates that it is slowing down.

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