Block moving down circle, a straight path, then into a 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.

Homework Equations

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.

 

[PeterO]

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.

Homework Equations

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?

 

[bfusco]

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.

 

[PeterO]

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

 

[asteriatic]

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