How to find the magnitude of the acceleration given F, kF, m

In summary, the conversation discusses a problem involving a block being pushed up a 30 degree incline with an applied force of 50 N. The block has a mass of 4.41 kg and a coefficient of kinetic friction of 0.4. The magnitude of the resulting acceleration on the block is being calculated, but there is confusion about how to approach the problem. The suggestion is made to draw a free body diagram and analyze the balance of forces on the block.
  • #1
Nairb
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<Moved from a technical forum and therefore no template.>

A block is pushed up a 30 incline by an applied force as shown. If F = 50 N and m = 4.41 kg and the coefficient of kinetic friction is 0.4. What is the magnitude of the resulting acceleration on the block?

This is what I did but it's wrong
Fnet= Fa-Fs
m*a= 50-0.2*4.41*9.8*cos(30 and then divide the whole thing by 4.41.
but the answer is wrong. What did I do wrong?
 
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  • #2
Welcome to Physics Forums.
I apologize, but I am having a difficult time understanding what you did. I will try to explain a couple of things. The force F = 48.5 is not acting in the direction of the acceleration. Only a component of it is. Also, the F = 48.5 N force also has the effect of increasing the normal force because a component of force F is acting perpendicular (edit: downward) to the plane of the surface.

Did you draw a free body diagram? For these types of problems, it is extremely helpful to draw a free body diagram. For this problem, I would assign the x-axis along the slope of the plane, and the y-axis perpendicular to that. That way, your acceleration will be entirely along the x axis.

Once you have your free body diagram, you will need to sum forces in the x direction and sum forces in the y direction. Then you can solve those 2 equations for the acceleration.
 
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  • #3
@Nairb, Is there an image to accompany the problem? It hard to check what's been tried without having a clear understanding of the actual scenario.
 
  • #4
gneill said:
Is there an image to accompany the problem?
Hmmm. There was an image originally. It seems that when the values were edited, the image disappeared. The force F was acting horizontally on the block that was sitting on a 30° incline.
 
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Sorry, the image was deleted by accident. Here it is:
img_secV3_q3.PNG

what I did was this: F - (uk*m*g*cos30) divided by the mass
 
  • #6
Nairb said:
F - (uk*m*g*cos30)
You need to analyse the balance of forces on the block more carefully.
What forces have components in the direction normal to the slope? What equation does that give?
Likewise for parallel to the slope.
 

1. What is the formula for finding the magnitude of acceleration given force, spring constant, and mass?

The formula for finding the magnitude of acceleration is a = F/km, where F is the force applied to the object, k is the spring constant, and m is the mass of the object.

2. How do I determine the units for acceleration in this equation?

The units for acceleration in this equation are meters per second squared (m/s²). This can be determined by looking at the units for force (Newtons) and mass (kilograms) and using the formula a = F/m.

3. Can this formula be used for any object, regardless of shape or size?

Yes, this formula can be used for any object as long as the force and mass are known and the object can be considered a point mass. However, if the object has a non-uniform shape or is rotating, a more complex formula may be needed.

4. How does the spring constant affect the acceleration of an object?

The spring constant (k) affects the acceleration of an object by determining how much the spring will stretch or compress in response to a given force. A higher spring constant means the spring is stiffer and will cause a greater acceleration on the object.

5. Is there a limit to how large or small the acceleration can be in this equation?

No, there is no limit to the magnitude of acceleration that can be calculated using this equation. However, keep in mind that it is always important to consider the practical limitations of the situation and to use common sense when interpreting the results.

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