# Block moving down circle, a straight path, then into a spring

• bfusco
In summary, the problem involves a block sliding along a track, starting from rest at point A and ending at point C where it compresses a spring. The section AB is a frictionless quadrant of a circle, while the section BC has a coefficient of kinetic friction of 0.27. The section CD is also frictionless. The task is to calculate the velocity at point B, the thermal energy produced as the block slides from B to C, the velocity at point C, and the stiffness constant k for the spring.
bfusco

## Homework Statement

Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 and is frictionless. B to C is a horizontal span 3.5 long with a coefficient of kinetic friction = 0.27. The section CD under the spring is frictionless. A block of mass 1.0 is released from rest at A. After sliding on the track, it compresses the spring by 0.35 .
A)calculate the velocity at point B.
B)Determine the thermal energy produced as the block slides from B to C.
C)calculate the velocity at point C.
D)determine the stiffness constant k for the spring.

## The Attempt at a Solution

A) i am having a hard time starting this question. for part A, i draw the free body diagram at the the top of the diagram (the side of the circle), i have the Normal force facing the center of the circle and the weight facing down. with that said i don't understand how to begin ƩF=mv^2/r equation in order to calculate the velocity.

bfusco said:

## Homework Statement

Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 and is frictionless. B to C is a horizontal span 3.5 long with a coefficient of kinetic friction = 0.27. The section CD under the spring is frictionless. A block of mass 1.0 is released from rest at A. After sliding on the track, it compresses the spring by 0.35 .
A)calculate the velocity at point B.
B)Determine the thermal energy produced as the block slides from B to C.
C)calculate the velocity at point C.
D)determine the stiffness constant k for the spring.

## The Attempt at a Solution

A) i am having a hard time starting this question. for part A, i draw the free body diagram at the the top of the diagram (the side of the circle), i have the Normal force facing the center of the circle and the weight facing down. with that said i don't understand how to begin ƩF=mv^2/r equation in order to calculate the velocity.

OK try these clarifying questions.

What energy transformation(s) occur in the A - B section?

What energy transformation(s) take place in the B - C section?

What energy transfer takes place after C?

PeterO said:
OK try these clarifying questions.

What energy transformation(s) occur in the A - B section?

What energy transformation(s) take place in the B - C section?

What energy transfer takes place after C?

from A - B the potential energy would go from its greatest value to 0, all that energy would become kinetic energy.

from B - C, the kinetic energy would decrease due to work done by friction.

after C, the object would hit the spring creating elastic potential energy.

Sorry about the lack of clarity, was in a rush when i posted and I am new at communicating over forums.

bfusco said:
from A - B the potential energy would go from its greatest value to 0, all that energy would become kinetic energy.

from B - C, the kinetic energy would decrease due to work done by friction.

after C, the object would hit the spring creating elastic potential energy.

Sorry about the lack of clarity, was in a rush when i posted and I am new at communicating over forums.

NO NO NO

The question was perfectly clear to me - and if you understand what you have just written, then you should be able to solve the problem

I would first analyze the given information and identify the key variables and equations that can be used to solve the problem. From the given information, we can identify the following variables:
- Radius of the circle (r = 2.0)
- Coefficient of kinetic friction (μ = 0.27)
- Length of the horizontal span (L = 3.5)
- Mass of the block (m = 1.0)
- Compression of the spring (x = 0.35)

To calculate the velocity at point B, we can use the conservation of energy principle. At point A, the block only has potential energy due to its height above the ground. As it moves down the circular path, it gains kinetic energy, which is then converted into potential energy as it compresses the spring. At point B, all of the block's energy is in the form of kinetic energy, so we can equate the initial potential energy to the final kinetic energy:

mgh = (1/2)mv^2

Where h is the height of point A above the ground, which is equal to the radius of the circle (r). Solving for v, we get:

v = √(2gh)

Substituting in the given values, we get:

v = √(2*9.8*2) = 6.26 m/s

To determine the thermal energy produced as the block slides from B to C, we need to calculate the work done by friction. The work done by friction is equal to the force of friction multiplied by the distance traveled:

W = Fd

The force of friction can be calculated using the equation F = μmg, where μ is the coefficient of kinetic friction, m is the mass of the block, and g is the acceleration due to gravity. The distance traveled is equal to the length of the horizontal span (L). Therefore, the work done by friction is:

W = μmgd = (0.27)(1.0)(9.8)(3.5) = 9.765 J

This is the thermal energy produced as the block slides from B to C.

To calculate the velocity at point C, we can use the conservation of mechanical energy principle again. At point C, all of the block's energy is in the form of potential energy, since it has come to a stop. Therefore, we can equate the final kinetic energy at

## 1. What is the concept of "Block moving down circle, a straight path, then into a spring"?

The concept refers to the motion of a block starting from a circular path, moving down in a straight line, and then being pushed into a spring where it experiences elastic deformation.

## 2. Why does the block move in a circular path initially?

The block moves in a circular path initially due to the presence of a centripetal force, which acts towards the center of the circle and keeps the block moving in a curved path.

## 3. How does the block move in a straight line after leaving the circular path?

Once the block leaves the circular path, the centripetal force is no longer acting on it. However, the block still maintains its tangential velocity, causing it to continue moving in a straight line due to inertia.

## 4. What happens when the block reaches the spring?

When the block reaches the spring, it experiences elastic deformation as the spring compresses. This is due to the force applied by the block on the spring, causing it to store potential energy in the form of elastic potential energy.

## 5. Can this concept be applied in real-life situations?

Yes, this concept can be applied in real-life situations such as roller coasters, where the initial circular path represents the curve of the track, the straight path represents the drop, and the spring represents the up and down motion of the cart due to the track's shape.

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