# Block hitting a spring down an incline

• AnkhUNC
In summary, the conversation discusses a block of mass 19 kg on a frictionless incline with a spring below it. The block compresses the spring by 3.6 cm and momentarily stops. The question asks for the distance the block moves down the incline and the speed of the block at the moment it touches the spring. The correct answer for (a) is 0.0290429321 meters. For (b), the equation v = sqrt(K*.036m^2)/19kg is used, but it is unclear if the sqrt covers the 19 in the denominator.
AnkhUNC

## Homework Statement

In Fig, a block of mass m = 19 kg is released from rest on a frictionless incline of angle θ = 34°. Below the block is a spring that can be compressed 4.5 cm by a force of 210 N. The block momentarily stops when it compresses the spring by 3.6 cm. (a) How far does the block move down the incline from its rest position to this stopping point? (b) What is the speed of the block just as it touches the spring?

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c08/fig08_41.gif

## The Attempt at a Solution

I found (a) = 0290429321 meters which is correct.
For (b) I tried the following v = sqrt(K*.036m^2)/19kg. But this is also incorrect. Any ideas?

AnkhUNC said:
I found (a) = 0290429321 meters which is correct.
For (b) I tried the following v = sqrt(K*.036m^2)/19kg. But this is also incorrect. Any ideas?

No decimal point for (a)?

For (b), your approach is correct, but I'm unable to make out if the sqrt covers the 19 in the denominator.

I would approach this problem by first analyzing the given information and identifying the relevant equations and principles that can be applied. From the given information, we can see that the block is released from rest on a frictionless incline and that the spring below it can be compressed by a force of 210 N. We also know the mass of the block and the angle of the incline. This information can be used to calculate the potential energy and kinetic energy of the block at different points during its motion.

To solve for (a), we can use the conservation of energy principle, which states that the total energy of a system remains constant. At the starting position, the block only has potential energy, which can be calculated using the equation PE = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the block on the incline. At the stopping point, the block has both potential and kinetic energy, which can be calculated using the equation KE = 1/2mv^2. By equating the potential energy at the starting point to the sum of potential and kinetic energy at the stopping point, we can solve for the distance traveled by the block.

To solve for (b), we can use the equation for the potential energy of a spring, PE = 1/2kx^2, where k is the spring constant and x is the displacement of the spring. We know that the spring is compressed by 3.6 cm, so we can solve for the spring constant using the given force of 210 N. Once we have the spring constant, we can use the equation for kinetic energy to solve for the velocity of the block just as it touches the spring.

In summary, to solve this problem as a scientist, we would use the principles of conservation of energy and the equations for potential energy and kinetic energy to solve for the distance traveled by the block and its velocity just as it touches the spring.

## 1. What is the purpose of studying a block hitting a spring down an incline?

The purpose of studying this phenomenon is to understand the principles of energy conservation and the behavior of objects on an inclined surface. It also allows scientists to explore the relationship between potential and kinetic energy.

## 2. How does the angle of the incline affect the block's motion?

The angle of the incline affects the block's motion by changing the amount of potential energy it has. A steeper incline will result in a greater potential energy, while a lower incline will result in a lower potential energy. This affects the block's speed and acceleration as it moves down the incline.

## 3. What is the role of the spring in this experiment?

The spring serves as a mechanism for storing and releasing potential energy. As the block hits the spring, it compresses and stores potential energy. When the spring expands, it releases this energy, causing the block to bounce back up the incline.

## 4. How does the mass of the block affect its motion?

The mass of the block affects its motion by changing the amount of kinetic energy it has. A heavier block will have more kinetic energy and therefore a higher velocity as it moves down the incline. However, the mass does not affect the relationship between potential and kinetic energy.

## 5. What factors can affect the accuracy of this experiment?

Some factors that can affect the accuracy of this experiment include air resistance, friction on the incline, and the elasticity of the spring. These factors can influence the amount of energy transferred and the final position of the block at the bottom of the incline.

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