Solving for Distance: Finding Work from Mass, Incline & Spring

In summary, the problem involves a 3kg mass traveling down a 30 degree frictionless incline and hitting a spring with k=400N/m. The spring contracts 0.2 meters and brings the block to a stop. To find the distance the block traveled, you can use the equation E = .5kx^2 to calculate the energy imparted to the spring. Then, using the conservation of energy principle, you can equate this energy to the potential energy of the block at the top of the incline, which can be found using the equation E = mgy. From there, you can use trigonometry to find the distance traveled by the block. The key to solving this problem is thinking and not
  • #1
UrbanXrisis
1,196
1
there's a 3kg mass on a 30 degree frictionless incline. The mass travels d distance and hits a spring with k=400N/m. The spring contracts 0.2 m and brings the block to a stop.

I need to find the distance the block traveled.

F=kx
F=400*.2
F=80N

so the block has to hit with 80N.
what formula would I use to get distance? I am confused because if I used any energy formula (which I know I will have to) the question is in Joules instead of Newtons. What should I do?
 
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  • #2
You can solve this with energy.
At any point on the block's path you can find its energy with the equation
[tex] E = .5kx^2 + .5mv^2 + mgy [/tex]

Consider when the spring has been fully compressed to be y=0. Can you do it from there? Note: y does not equal d.
 
  • #3
are you saying that:
E=80N+.5mv^2 ?
 
  • #4
Heres the easiest way to solve the problem:
We know the spring compressed .2 meters. How much energy did the block impart to the spring to do this? We can find out using the potential energy of a spring formula [tex] E = .5kx^2 [/tex] Under the conservation of energy, the potential energy of the block at the top of the ramp must be equal to the PE of the spring. Use [tex] E = mgy [/tex] to find y and then use trigonometry to find the hypotonuese of the triangle.
Remember : the key to sucsess in physics is thinking; not memorizing how to do every possible problem.
 

1. How do you calculate the distance using mass, incline, and spring?

To calculate the distance using mass, incline, and spring, you will need to use the formula: Distance = (Work)/(Force x Incline). The work can be found by multiplying the force applied by the displacement. The force can be calculated by multiplying the mass by the acceleration due to gravity. The incline is the angle of the ramp or slope.

2. What is the role of mass in solving for distance?

Mass plays a crucial role in solving for distance as it affects the amount of force needed to move an object. The greater the mass, the more force is required to move it. This relationship is represented in the formula: Force = Mass x Acceleration.

3. How does the incline affect the distance calculation?

The incline affects the distance calculation by increasing the force needed to move an object. The steeper the incline, the greater the force required to move the object. This is taken into account in the formula: Distance = (Work)/(Force x Incline).

4. Can the distance calculation be affected by the type of spring used?

Yes, the type of spring can affect the distance calculation. Different types of springs have different levels of stiffness or spring constant, which can affect the amount of work required to compress or stretch it. This can change the overall calculation for distance.

5. How can this formula be applied in real-life situations?

This formula can be applied in many real-life situations, such as determining the distance traveled by a car moving up an inclined road, or calculating the distance a weightlifter lifts a barbell up a ramp. It can also be used in engineering and physics experiments to determine the work done on an object by a force applied at an angle.

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