Force Spring Compression of 13kg Block on 35° Incline

In summary: So, you need to find the value of x.In summary, a 13.0 kg block slides down a 35.0° incline without friction and is stopped by a strong spring with k = 2.60 x 10^4 N/m. After sliding 3.00 m, the block comes to rest. To find the compression of the spring, we can use energy considerations and the force exerted by the spring (kx). By setting the gravitational potential energy of the block equal to the energy stored in the compressed spring, we can solve for the compression (x).
  • #1
_mae
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Homework Statement


A block of mass 13.0 kg slides from rest down a frictionless 35.0° incline and is stopped by a strong spring with k = 2.60 x 10^4 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?


Homework Equations



F=mg (weight of block in Newtons)


The Attempt at a Solution


I've found the weight of the block in Newtons (127.4 N), and I know that I have to find the force of the spring in its direction. To get the final answer, I'd have to divide that by the value of k. But I don't know how to find the force of the spring!
 
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  • #2
would that be momentary rest as the spring compresses to its maximum, before shooting the block back up, or the rest after all oscillations have died down? The former I guess.

Have you ried using energy considerations instead...consider the enrgy changes in the block and the energy stored in the spring.
 
  • #3
The whole weight of the block is not pushing against the spring – just its component along the plane.

The block had only grav PE when it started. Where is that gone now? Take x as the compression in the spring and write the proper energy eqn.

The force exerted by the spring is kx.
 

1. What is force spring compression?

Force spring compression is the amount of force applied to a spring that results in the spring being compressed or compressed further. This force can be measured in units of newtons (N) or pounds (lbs), depending on the unit system used.

2. How is force spring compression calculated?

Force spring compression is calculated using the equation F = kx, where F is the force applied to the spring, k is the spring constant, and x is the amount of compression or displacement of the spring. The spring constant represents the stiffness of the spring and is measured in units of newtons per meter (N/m) or pounds per inch (lbs/in).

3. What is a 13kg block?

A 13kg block refers to a block or object with a mass of 13 kilograms. Mass is a measure of the amount of matter in an object and is typically measured in units of kilograms (kg) or grams (g). It is an important factor in calculating force, as described by Newton's second law: F = ma, where F is the force, m is the mass, and a is the acceleration.

4. How does the 35° incline affect the force spring compression of a 13kg block?

The 35° incline affects the force spring compression of a 13kg block by changing the direction and magnitude of the force acting on the block. When the block is placed on an incline, the force of gravity acting on the block is split into two components: one that is perpendicular to the incline (normal force) and one that is parallel to the incline (force of gravity). This change in force direction can affect the amount of compression in the spring.

5. How is force spring compression used in scientific research?

Force spring compression is used in scientific research to study the properties of materials and to test the strength and elasticity of various objects. It is also commonly used in experiments involving springs and other elastic objects, as well as in fields such as mechanical engineering and materials science.

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