Reviewing for my exam (Newton question)

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In summary, the conversation discusses pushing a 20 kg box up a hill with a force of 200 N for 6 m, resulting in the box accelerating from rest to 2 m/s. A 100 N frictional force opposes the motion. The energy bar charts are used to describe the system, and the box is at an elevation of 2.86 m when it reaches a speed of 2 m/s. The hill makes an angle of approximately 25.5 degrees with the horizontal.
  • #1
Chandasouk
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Homework Statement



You push a 20 kg box from an elevation of zero up a hill. You exert a force of 200 N for 6 m and the box speeds up steadily from rest to 2 m/s. There is a 100 N frictional force that opposes the box’s motion.

A) Draw energy bar charts to describe this motion. Be sure to describe your system, and the initial and final states.

B) At what elevation is the box moving when its speed is 2 m/s?

C) What angle does the hill make with the horizontal?






A) Initial (Bottom) Work = Final (Top) PE + KE+ [tex]\Delta[/tex]Uinternal

B) Givens

m=20kg
F-applied = 200N
F-friction = 100N
V = 2m/s
L(distance traveled) = 6m

H= ?

Fd = mgh + .5mv2 + [tex]\Delta[/tex]Uinternal

(200N)(6m) = (20kg)(9.80m/s^2)h + .5(20kg)(2m/s)^2 + (100N)(6m)

1200J = 196h + 40J + 600J

600J = 196h + 40J

560J = 196h

H = 2.86m


C) tan[tex]\theta[/tex] = 2.86/6 = 25.5 degrees

Not sure if anything is correct to be honest.
 
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  • #2
Actually I think that's about right. Just make sure you're using the right trigonometric function for the last step.
 
  • #3



I can provide a response to the above content by offering some corrections and clarifications.

Firstly, in part A, the energy bar charts should show the initial and final energies of the system, not states. The system in this case is the box and the hill, and the initial state is when the box is at rest at the bottom of the hill, while the final state is when the box has reached a speed of 2 m/s at a certain elevation on the hill.

In part B, the calculation for the elevation is incorrect. The correct equation should be:

Fd = mgh + .5mv2 + ΔUinternal

(200N)(6m) = (20kg)(9.8m/s^2)h + .5(20kg)(2m/s)^2 + (100N)(6m)

1200J = 196h + 20J + 600J

580J = 196h

h = 2.96m

Therefore, the box is moving at a speed of 2 m/s when it is at a height of 2.96 meters on the hill.

In part C, the angle of the hill can be found using the equation:

tanθ = h/L

tanθ = 2.96/6 = 0.493

θ = arctan(0.493) = 26.7 degrees

Therefore, the hill makes an angle of approximately 26.7 degrees with the horizontal.

It is important to double-check calculations and equations to ensure accuracy in scientific work. Also, it would be helpful to provide units for all values to avoid confusion and ensure correct calculations.
 

1. How did Newton contribute to the field of science?

Newton is most famously known for his three laws of motion, which laid the foundation for classical mechanics. He also made significant contributions to the study of optics, mathematics, and gravity.

2. What are Newton's three laws of motion?

Newton's first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

3. How did Newton's laws of motion impact our understanding of the universe?

Newton's laws of motion revolutionized the way we understand and predict the behavior of objects in the universe. They provided a mathematical framework for describing the motion of objects, and they also helped to explain phenomena such as gravity and the movement of planets.

4. What is the difference between Newton's laws of motion and Einstein's theory of relativity?

While Newton's laws of motion describe the behavior of objects in the macroscopic world, Einstein's theory of relativity applies to the macroscopic and microscopic worlds. It explains the relationship between space and time and how they are affected by the presence of mass and energy.

5. How can I apply Newton's laws of motion to solve problems on my exam?

To apply Newton's laws of motion, you must first identify the forces acting on the object, then use the appropriate equation to calculate the acceleration or any other unknown variables. It is also important to draw clear diagrams and label all known and unknown quantities to help organize your thoughts and calculations.

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