Finding acceleration of a block being pushed up a ramp by a horizontal force

In summary, the block is being pushed up a frictionless incline with an applied horizontal force. The acceleration of gravity is 9.8 m/s^2 and the magnitude of the resulting acceleration of the block is unknown. By using the equations for a right triangle on a Free Body Diagram and the formula F=ma, the net force and acceleration of the block can be calculated. However, there was an error in the calculation of the values for x and v, resulting in an incorrect answer. The correct values can be found by learning how to find the components of a vector."
  • #1

Homework Statement


A block is pushed up a frictionless incline by
an applied horizontal force as shown.
The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the resulting acceleration of the block?
Answer in units of m/s^2.


Homework Equations


Sin(theta)=opposite/hypotenuse
Cos(theta)=adjacent/hypotenuse
Tan(theta)=opposite/adjacent
^^^^^^^^^above equations for a right triangle on a Free Body Diagram
F=ma

The Attempt at a Solution


So if i extend the block's line and make a right triangle with that line and the line of the applied force, i know the theta of that triangle is equal to the ramp's, 34. I can also make a right triangle using gravity and its two vectors, one along the ramp and one perpendicular to the ramp. That triangle's theta is also 34. So to find the acceleration of the block, i need to subtract x from v (See attached picture). But i can't prove the two triangles are congruent, because the gravity vector triangle has only two known values while the force vector triangle has only 1. Help!
 

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  • #2
Wait, i got a little further on the problem.
Knowing that gravity is 9.8, i can find x and y of the gravity vector triangle.
x=sin(theta)g=~5.480090454
y=cos(theta)g=~8.124568211
SO now i know x.
I need to find v to get the net force, how?
 
  • #3
cellfoneguy said:
I need to find v to get the net force, how?
The same principles that apply to one right triangle will apply to another. If you can relate mg to y, you can relate z to v.
 
  • #4
ok i used the formula to calculate v and x. Then using f=ma, i found the acceleration. I was wrong.
I found a mistake, in that in the gravity vector triangle, i used 9.8 which is in m/s^2. After converting it to Newtons, i get that x is 20 something Newtons, which cannot be correct, because then the net force is negative, meaning the block is going down the ramp. However, the problem states the block is going up the ramp. whaaaaat?
 
  • #5
Yes, given the values in the diagram, the net force is down the plane. Are you sure the problem stated that the block is moving up the plane? Or did it just say that it was being pushed up the plane (meaning that the push has a component up the plane)?
 
  • #6
Well, i took x (11.18385807)-v (30.06090238) and got -18.87704431 N. Then i divided by 3.7 (the mass) and got 5.101903868, which is wrong. What?
 
  • #7
cellfoneguy said:
Well, i took x (11.18385807)-v (30.06090238) and got -18.87704431 N.
Your values for x and v are incorrect.
 
  • #8
i agree that the answer is a net force acting down the slope of the hll
 
  • #9
are the correct values
13.746065934159120354149637745012 for x
and
5.4800904540133189355721957718627 for v?
 
  • #10
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1. How do you calculate the acceleration of a block being pushed up a ramp by a horizontal force?

The acceleration of a block being pushed up a ramp by a horizontal force can be calculated using the formula a = (Fsinθ - μmgcosθ)/(m + msinθ), where F is the applied horizontal force, θ is the angle of the ramp, μ is the coefficient of friction, m is the mass of the block, and g is the acceleration due to gravity.

2. What factors affect the acceleration of a block being pushed up a ramp by a horizontal force?

The acceleration of a block being pushed up a ramp by a horizontal force is affected by the magnitude and direction of the applied force, the angle of the ramp, the coefficient of friction between the block and the ramp, and the mass of the block.

3. How does the angle of the ramp affect the acceleration of a block being pushed up a ramp by a horizontal force?

The angle of the ramp affects the acceleration of a block being pushed up a ramp by a horizontal force by changing the component of the force that acts in the upward direction. As the angle increases, the component of the force acting in the upward direction decreases, leading to a decrease in acceleration.

4. What is the role of friction in determining the acceleration of a block being pushed up a ramp by a horizontal force?

Friction plays a significant role in determining the acceleration of a block being pushed up a ramp by a horizontal force. The coefficient of friction between the block and the ramp affects the normal force acting on the block, which in turn affects the acceleration. A higher coefficient of friction will result in a larger normal force and therefore a smaller acceleration.

5. Can the acceleration of a block being pushed up a ramp by a horizontal force ever be greater than the applied force?

No, the acceleration of a block being pushed up a ramp by a horizontal force can never be greater than the applied force. This is because the maximum acceleration possible is limited by the weight of the block and the frictional forces acting on it. Therefore, the applied force can only contribute to a certain extent towards the acceleration of the block.

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