How far does a block travel before hitting a spring?

In summary, a block with a mass of 33.0 kg starts from rest at the top of a 31.0 degree inclined plane and encounters a spring with a constant of 3.4 kN/m attached to the plane. The spring is compressed by 37.0 cm and has a potential energy of 232.73 J. The distance traveled by the block before encountering the spring is found by using the equation mgy = Us, taking into consideration the 37 cm of compression.
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Homework Statement


A block starts from rest at the top of a 31.0 degree inclined plane and encounters a spring, of constant 3.4 kN/m, rigidly attached to the plane. If the block's mass is 33.0 kg and it compresses the spring by 37.0 cm, find the distance the block traveled before it encountered the spring.


Homework Equations





The Attempt at a Solution



The spring compresses to 37cm, and has a spring constant of 3,400 kN. So I solve for U_s, the potential energy of the spring, and get U_s = 232.73 J.

Since friction is not mentioned, I know that the potential energy at the top of the incline equals U_s. Or, mgy = 232.73J, or (33)(9.8)y = 232.73. I use trig and solve for the distance travelled, but it doesn't match the answer of the problem. What am I doing wrong?

Thank you
 
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  • #2
When you solved for the distanced traveled, did you take into consideration the 37 cm? (They want the distance traveled before hitting the spring.)
 
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That's it. Thank you
 

1. How does the distance traveled by a block before hitting a spring depend on its initial velocity?

The distance traveled by a block before hitting a spring is directly proportional to its initial velocity. This means that the faster the block is moving, the further it will travel before hitting the spring.

2. Does the mass of the block affect how far it will travel before hitting a spring?

The mass of the block does not have a significant impact on the distance it travels before hitting a spring. As long as the block has enough initial velocity to reach the spring, its mass will not affect the distance traveled.

3. What role does the spring constant play in determining the distance traveled by a block before hitting a spring?

The spring constant, which is a measure of the stiffness of the spring, affects how far the spring will be compressed when the block hits it. This, in turn, affects the distance the block will travel before hitting the spring.

4. Is the distance traveled by a block before hitting a spring affected by the angle at which it is released?

Yes, the angle at which the block is released can affect the distance it travels before hitting the spring. If the block is released at an angle, it will have a horizontal and vertical component of velocity, which will affect its trajectory.

5. What factors, other than those mentioned, can affect the distance traveled by a block before hitting a spring?

Some other factors that can affect the distance traveled by a block before hitting a spring include air resistance, friction, and the height from which the block is released. These factors can slightly alter the trajectory of the block and affect the distance it travels before hitting the spring.

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