Block down ramp colliding with spring

In summary: Uspring = 1/2 kx^2.In summary, to find the maximum compression of a spring released from a 3.2-kg block 34m away, with a force constant of 178N/m on a frictionless plane inclined at an angle of 27° above the horizontal, use energy conservation to set up a quadratic equation. Measure gravitational potential energy from the lowest point and use the equation Ugrav = mgd sin(theta) and Uspring = 1/2 kx^2 to find the maximum compression.
  • #1
TraceBusta
35
0
A 3.2-kg block is released 34m from a massless spring with force constant 178N/m that is fixed along a frictionless plane inclined at an angle of 27° above the horizontal. Find the maximum compression of the spring.

This is what I have tried so far.
equation (1) (1/2 mv^2) = (1/2 kx^2)

equation (2) (1/2 mv^2)=d*mg(sin theta)

i used equation (2) to solve for v.
then using that value of v i solved (1)

my answer for x=2.333 meters, however that is wrong
 
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  • #2
In calculating the gravitational PE, don't forget to include the distance the block falls in compressing the spring a distance X.
 
  • #3
ok, i think i understand the concept of that, but I'm not sure how I would set that up in equation form. Because gravity works in the y-component, would i have to use 2 equations. 1 to include for the y-distance the spring compresses and another to solve for the total compression in the sin (theta) component of the spring? If that was the case then I don't know how to set those up because i am trying to solve for maximum compression and in the first equation i woul dneed to know that.
 
  • #4
Think of it this way: How far does the block slide? d = 34m + x. (x = how far the spring compresses.) Use energy conservation: Intial energy (gravitational PE) = final energy (spring PE). You'll get a quadratic equation.

Hint: measure gravitational PE from the lowest point.
 
  • #5
i set up the problem like this
U=mg(h+x sin (theta))
Uspring=1/2 k x^2

so mg(h+x sin (theta)) = 1/2 kx^2?

solving for x, x1=1.1331, x2=-1.0965
those are both wrong.
 
  • #6
Ugrav = mgd sin(theta), where d = 34m +x
 

1. What is the purpose of studying "Block down ramp colliding with spring"?

The purpose of studying "Block down ramp colliding with spring" is to understand the dynamics and behavior of objects in motion, specifically in the context of collisions. This can provide insights into real-world scenarios such as car crashes or impacts between objects in a manufacturing setting.

2. How does the mass of the block affect the resulting collision with the spring?

The mass of the block affects the collision with the spring in two ways. First, a heavier block will have more inertia, meaning it will be more resistant to changes in its motion. This can result in a stronger collision with the spring. Second, a heavier block will also experience a greater change in velocity during the collision, leading to a larger change in kinetic energy.

3. What factors influence the height the block reaches after colliding with the spring?

The height the block reaches after colliding with the spring is influenced by several factors, including the initial height and speed of the block, the spring constant, and the mass of the block. In addition, external factors such as air resistance and friction can also play a role in determining the height reached.

4. Can the block and spring collision be modeled mathematically?

Yes, the block and spring collision can be modeled mathematically using principles of conservation of energy and momentum. By considering the initial and final states of the system, equations can be derived to calculate the resulting velocity, height, and other parameters of the block and spring after the collision.

5. How does the angle of the ramp affect the collision between the block and spring?

The angle of the ramp can affect the collision between the block and spring in several ways. A steeper ramp will result in a greater change in height and velocity of the block, potentially leading to a stronger collision with the spring. Additionally, the angle can also affect the direction and magnitude of the force exerted by the ramp on the block during the collision.

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