Spring Problem On inclined plane without numbers, only variables

In summary, the conversation discusses the relationship between spring energy and work done by friction on a block moving up a ramp. By setting the energy left equal to gravitational potential energy and using mathematical equations, the height (h) can be solved for in terms of x and sine. A small error was noted in the second term of the numerator, but overall the calculations were correct.
  • #1
Jaccobtw
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Homework Statement
A spring of spring constant k is attached to a support at the bottom of a ramp that makes an angle (theta) with the horizontal. A block of inertia m is pressed against the free end of the spring until the spring is compressed a distance d from its relaxed length. Call this position A. The block is the released and moves up the ramp until coming to rest at position B. The surface is rough from position A for a distance 2d up the ramp, and over this distance the coefficient of kinetic friction for the two surfaces is (μ). Friction is negligible elsewhere. What is the distance from A to B?
Relevant Equations
E(spring) = (1/2)kd^2
E(gravitational) = mgh
E(Work done by friction = μF(normal) *(distance)
So we know that all the energy originates from the spring:

E(spring) = (1/2)kd^2

As the block moves up the ramp, friction does work on the block over a distance of 2d:

W = μmgcos(θ)* 2d

So subtracting the work done by friction from the spring energy, gives us the energy left, so we'll set it equal to mgh

(1/2)kd^2 - μmgcos(θ) * 2d = mghSpring Energy - Work = Gravitational Potential Energy

Use math to get the height (h) in terms of x and sine = mgh = xmgsin(θ)

Now solve for x:

x = ((1/2)kd^2 - 2dμmgcos(θ)) / (mgsin(θ))

I'm trying to figure out what I did wrong if anything.
 
Last edited:
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  • #2
Your work looks good to me.
Jaccobtw said:
Now solve for x:

x = ((1/2)kd^2 - 2μmgcos(θ)) / (mgsin(θ))
You dropped a factor of d in the second term of the numerator. But that's probably just a typing error.
 
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Related to Spring Problem On inclined plane without numbers, only variables

Question 1: What is a spring problem on an inclined plane without numbers, only variables?

A spring problem on an inclined plane without numbers, only variables, is a physics problem that involves a spring (a device that stores and releases energy) and an inclined plane (a flat surface that is tilted at an angle). This type of problem requires the use of mathematical variables to represent the unknown quantities.

Question 2: What are the variables involved in a spring problem on an inclined plane without numbers?

The variables involved in a spring problem on an inclined plane without numbers can include the mass of the object attached to the spring, the spring constant (a measure of the stiffness of the spring), the angle of the inclined plane, and the displacement of the spring from its equilibrium position.

Question 3: How do you solve a spring problem on an inclined plane without numbers?

To solve a spring problem on an inclined plane without numbers, you can use the basic principles of physics, such as Hooke's law (which relates the force exerted by a spring to its displacement) and Newton's laws of motion (which describe the relationship between an object's mass, acceleration, and applied forces). You will also need to use algebraic equations to represent the variables and solve for the unknown quantities.

Question 4: How is the angle of the inclined plane important in a spring problem?

The angle of the inclined plane is important in a spring problem because it affects the gravitational force acting on the object attached to the spring. This force, along with the force exerted by the spring, determines the net force and acceleration of the object.

Question 5: What are some real-world applications of spring problems on inclined planes?

Spring problems on inclined planes have many real-world applications, such as in engineering (for example, designing a shock absorber for a car), sports (such as calculating the trajectory of a ski jumper), and construction (for determining the strength of materials used in buildings). They are also commonly used in physics experiments to study the behavior of springs and inclined planes.

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