Ramps and Newton's Second Law

In summary, when calculating the normal force, you need to find the component of gravity that is perpendicular to the ramp. The gravity is Fg.
  • #1
swede5670
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0

Homework Statement


The 60 kg block starting at rest is pushed 7.8 m up a ramp at an angle θ = 26.5° to the horizontal in 15 s. If the coeficient of kinetic friction is 0.17:
What is the acceleration of block?
What is the force used to push the block up the ramp?

Homework Equations


Fnet = ma
Delta X = Vit + (1/2)at^2
Fg=ma
Fkinetic = μ * N

The Attempt at a Solution


I think I understand the first part,
7.8 = 0*15 + (1/2)(a)(15^2)
7.8 = 112.5a
.069=a

But the second part is what's giving me trouble
Do I need to make an Fnet = ma equation?
If I do I know that it would look like this
Force of Push - Force of friction = ma
Force of Push - Force of friction = (60)(.069)
Can I substitute in this equation? Fkinetic = μ * N for Fk?
Force of Push - (μ * N) = 60* .069
Fpush - (.17 * N) = 4.14

But what is my N force? I think that it would just be mass times acceleration of gravity and in that case:
Fpush - (.17 * (60 * 9.81)) = 4.14
Fpush - 100.06200 = 4.14
Fpush = 104.20200N

I'm not sure if this is right, I appreciate your help in advance.
 
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  • #2
You did the first part right.

For the second part, you did everything right except your calculation of the normal force. Try drawing a force diagram of the block. On an inclined ramp, gravity doesn't act perpendicular to the plane of motion.
 
  • #3
Do I just need to find the horizontal component of gravity?
 
  • #4
Not the horizontal component, though you do need to break gravity into components. You need to find the component of gravity that is perpendicular to the ramp.
 
  • #5
So then do I just do
Cosine (26.5) = A/H
and in this case adjacent is the force I am looking for and H is gravity
Is the gravity Fg? so I can substitute Fg=ma
60 * 9.81 = Fg

Then I have
Cosine (26.5) * (60 * 9.81) = A

Is this correct?
 
  • #6
Alright well that's wrong and I'm not sure why
Cos(26.5) * H = A
Cos(26.5) * (60 x 9.81) = A
which ends up being 118.71N
When I plug that in I get
Fpush - (.17 x 118.97) = 4.14
Fpush = 24.36
And I this doesn't work, so I'm not sure what's going wrong
 

1. What is Newton's Second Law?

Newton's Second Law, also known as the Law of Force and Acceleration, states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In simpler terms, the more force applied to an object, the greater its acceleration will be. This law is expressed by the famous equation F=ma, where F is force, m is mass, and a is acceleration.

2. How does Newton's Second Law apply to ramps?

When an object is on a ramp, the force of gravity acting on it is split into two components: the force parallel to the ramp and the force perpendicular to the ramp. The force parallel to the ramp is what causes the object to accelerate down the ramp, while the force perpendicular to the ramp does not contribute to acceleration. According to Newton's Second Law, the acceleration of the object down the ramp is directly proportional to the force parallel to the ramp and inversely proportional to its mass.

3. What is the relationship between the angle of a ramp and the acceleration of an object?

As the angle of a ramp increases, the force parallel to the ramp also increases. This means that the object will accelerate down the ramp at a faster rate. However, the force perpendicular to the ramp remains the same regardless of the angle. This means that the mass of the object will also affect its acceleration down the ramp. A heavier object will experience a smaller acceleration than a lighter object on the same ramp at the same angle.

4. How does friction play a role in the application of Newton's Second Law on ramps?

Friction is a force that opposes motion, and it can act on an object on a ramp. This means that the force parallel to the ramp must also overcome the force of friction in order for the object to accelerate down the ramp. The amount of friction depends on the roughness of the ramp's surface and the weight of the object. The greater the friction, the more force will be needed to accelerate the object.

5. How does changing the length of a ramp affect the acceleration of an object?

According to Newton's Second Law, the length of a ramp should not affect the acceleration of an object. As long as the angle of the ramp remains the same, the force parallel to the ramp and the force perpendicular to the ramp will also remain the same. This means that the acceleration of the object down the ramp will not change. However, if the length of the ramp changes, the distance the object travels will change, affecting its final velocity.

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