Newton's laws and incline surfaces

In summary: Good job!In summary, the question is asking for the distance a box will travel up a 20 degree incline with an initial velocity of 5m/s before coming to rest. The correct solution involves finding the parallel component of the weight, using trigonometry to find the angle of the incline, and then using a kinematic equation to solve for the distance traveled. The final answer is approximately 3.37 meters.
  • #1
naada
4
0

Homework Statement



A box is given an initial velocity of 5m/s up a smooth 20 incline surface . The distance the box travel before coming to rest is?


Homework Equations



I can't solve it correctly , I can't get the idea of this question

The Attempt at a Solution



x= ?
vi=5
v=0
a=?

F = ma
mg cos ? = a

tan-1 20 = 87.14
180 = 90 + 87.14 + ?
?= 180 -90-87.14
?=2.9

(mg cos 2.9 = ma ) /m
g cos 2.9 = a
a= 28.03

x = 25 /( 28.03 )2
x= 0.45 m

My answer is so wrong !
But i can't figure out how to solve this problem
 
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  • #2
naada said:
A box is given an initial velocity of 5m/s up a smooth 20 incline surface .
Presumably a 20 degree incline?


F = ma
mg cos ? = a
What's the component of the weight acting down the incline?

tan-1 20 = 87.14
180 = 90 + 87.14 + ?
?= 180 -90-87.14
?=2.9
Not sure what you're doing here. I presume that the angle is given as 20 degrees.

(mg cos 2.9 = ma ) /m
g cos 2.9 = a
a= 28.03
You have the wrong angle (and trig function).


x = 25 /( 28.03 )2
x= 0.45 m
Sanity check: The acceleration due to gravity is only 9.8 m/s^2, so how can the acceleration parallel to the incline be greater than that?

Find the correct acceleration and that kinematic equation will work.

Read this to learn how to handle inclined planes: http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm" [Broken]
 
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  • #3
Presumably a 20 degree incline?

the question didn't mention the word "degree" or " ْ "
it's exactly as I wrote it .
So I toke 20 as the slop

#
x=? vi=5 vf=0 a=?

F = ma
(m g cos20 = m a) / m
9.8 cos20 = a
a=9.21

x=25/(2a)
x=25/(18.42)
x=1.37 m
Which is also wrong

#
180 = 90+20+?
180 -90-20=70ْ

F= m a
(m g cos 70 = m a)/m
9.8 cos 70 = a
a=3.35

x=25/(2a)
x=25/(2*3.35)
x=3.37 m
I think this one is the right one,but not sure.

thanks for the link was so useful
 
  • #4
naada said:
Presumably a 20 degree incline?

the question didn't mention the word "degree" or " ْ "
it's exactly as I wrote it .
So I toke 20 as the slop
I would take it to mean a 20 degree angle to the horizontal.

#
x=? vi=5 vf=0 a=?

F = ma
(m g cos20 = m a) / m
9.8 cos20 = a
a=9.21

x=25/(2a)
x=25/(18.42)
x=1.37 m
Which is also wrong
It's wrong because you took cos20, which is the component perpendicular to the incline. You need the parallel component.


#
180 = 90+20+?
180 -90-20=70ْ

F= m a
(m g cos 70 = m a)/m
9.8 cos 70 = a
a=3.35

x=25/(2a)
x=25/(2*3.35)
x=3.37 m
I think this one is the right one,but not sure.
This time you used the correct acceleration (which is g sin20), but you made a small error in your final calculation--probably a typo. (Redo the very last step.)

Other than that minor problem, you got it right.
 

1. What are Newton's laws of motion?

Newton's laws of motion are three fundamental principles that describe the motion of objects. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law states that the force applied to an object is equal to its mass multiplied by its acceleration. The third law states that for every action, there is an equal and opposite reaction.

2. What is an inclined surface?

An inclined surface is a surface that is angled or sloped, rather than being flat or horizontal. In physics, inclined surfaces are often used to study the effects of gravity on objects.

3. How do Newton's laws apply to objects on inclined surfaces?

Newton's laws apply to objects on inclined surfaces in the same way they apply to objects on flat surfaces. The first law still holds true, as the object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law also still applies, but the force of gravity must be taken into account when calculating acceleration. The third law also remains unchanged, as for every force the object exerts on the surface, the surface exerts an equal and opposite force on the object.

4. What is the relationship between the angle of an inclined surface and the force of gravity?

The angle of an inclined surface affects the force of gravity on an object by changing the direction of the force. As the angle increases, the force of gravity acting on the object becomes more perpendicular to the surface, resulting in a greater force pulling the object down the incline.

5. How do inclined surfaces affect the motion of objects?

Inclined surfaces can affect the motion of objects by changing the direction and magnitude of the force acting on the object. The steeper the incline, the greater the force of gravity acting on the object, and therefore, the faster the object will accelerate down the incline. The incline can also change the direction of the object's motion, causing it to move in a different direction than it would on a flat surface.

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