How Is Maximum Speed Calculated for a Block on a Vertical Spring?

[Dauden]

Homework Statement

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/spring/homework/Ch-08-GPE-ME/mass_vertical_spring/7.gif

A spring with spring constant k = 40 N/m and unstretched length of L0 is attached to the ceiling. A block of mass m = 1 kg is hung gently on the end of the spring.


Now the block is pulled down until the total amount the spring is stretched is twice the amount found in part (a). The block is then pushed upward with an initial speed vi = 4 m/s.

What is the maximum speed of the block?

Homework Equations

KE = (1/2)mv^2
PE = (1/2)kx^2

The Attempt at a Solution

Well, the answer for part a) they want me to use is .245 m. The way I set this up was:

(1/2)mv^2 = (1/2)mvi^2 + (1/2)kx^2

(1/2)(1)v^2 = (1/2)(1)(4^2) + (1/2)(40)(.49^2)

I did this because the kinetic energy at the maximum speed point should be equal to the potential plus the kinetic energy given by the push. When I solve for v on the left side I get 5.06 m/s but that is wrong.

 

[tiny-tim]

Hi Dauden!

Well, the answer for part a) they want me to use is .245 m. The way I set this up was:

(1/2)mv^2 = (1/2)mvi^2 + (1/2)kx^2

(1/2)(1)v^2 = (1/2)(1)(4^2) + (1/2)(40)(.49^2)

I did this because the kinetic energy at the maximum speed point should be equal to the potential plus the kinetic energy given by the push. When I solve for v on the left side I get 5.06 m/s but that is wrong.

No, KE_max - KE₀ = PE₀ -PE_max …

and you haven't mentioned gravity

 

[nlightner]

I would approach this problem by first identifying the known variables and the relevant equations to use. In this case, the known variables are the mass of the block, the spring constant, the initial speed, and the maximum stretch of the spring. The relevant equations to use are the equations for kinetic energy and potential energy.

Next, I would carefully set up the equations and plug in the known values to solve for the maximum speed of the block. It is important to pay attention to units and use the correct values in the equations.

After getting a numerical answer, I would double check my calculations and make sure they make sense in the context of the problem. If the answer seems incorrect, I would go back and check my equations and calculations to find any mistakes.

Lastly, I would consider the significance of the answer and any potential sources of error. In this case, the maximum speed of the block is important because it tells us the maximum speed the block will reach after being pushed upwards. However, there may be some sources of error in the calculations, such as neglecting air resistance or assuming a perfectly ideal spring. These potential errors should be acknowledged and considered when interpreting the results.