How Far Back Must the Spring Be Pulled to Swing the Masses Around the Pivot?

  • Thread starter Thread starter Mercfh
  • Start date Start date
  • Tags Tags
    Rotational Spring
Click For Summary
SUMMARY

The discussion centers on calculating the necessary displacement (∆x) of a spring to launch a 0.2 kg mass, with a spring constant of 1000 N/m, so that it can swing a combined mass of 0.5 kg (0.2 kg + 0.3 kg) around a pivot. The mass travels 1 m across a surface with a coefficient of kinetic friction (µk) of 0.2 before colliding with another mass. The key equations involved include the minimum velocity required to complete a loop (V_min = sqrt(5gR)) and the spring distance launched (d = Kx^2/(2mugm)). The discussion emphasizes the importance of calculating the velocity after the spring launch and ensuring it meets the minimum velocity for the swing.

PREREQUISITES
  • Understanding of spring mechanics and Hooke's Law
  • Knowledge of kinetic friction and its effects on motion
  • Familiarity with gravitational potential energy concepts
  • Basic proficiency in solving physics equations involving mass and acceleration
NEXT STEPS
  • Calculate the minimum velocity required to swing the combined masses around the pivot using V_min = sqrt(5gR)
  • Determine the velocity of the 0.2 kg mass after traveling 1 m considering kinetic friction
  • Explore the relationship between spring displacement and kinetic energy using d = Kx^2/(2mugm)
  • Investigate gravitational potential energy changes during the swing of the combined masses
USEFUL FOR

Physics students, educators, and anyone interested in mechanics, particularly those studying spring dynamics and motion under friction.

Mercfh
Messages
1
Reaction score
0

Homework Statement


A 0.2 kg mass is held against a spring with spring constant k=1000N/m. It is launched from the spring
and travels an additional 1 m across a surface with coefficient of kinetic friction µk=0.2. It then collides
and sticks to a 0.3 kg mass that is suspended from a 0.5 m long thread of negligible mass. How far back
must the spring be pulled (∆x) in order that the combined masses swing fully around the support pivot?

Homework Equations


Velocity Min to get around a loop= sqrt(5gR)
Spring Distance Launched= d = Kx^2/(2mugm)
Velocity of a Spring? = V^2=(k/m)*d^2
Distance = x = V^2/2a
Acceleration = m*g


The Attempt at a Solution


Well I wasn't sure if the Velocity equation was the "right" equation to find this. ideally I would "think" you would find the minimum speed that the spring would launch...but this doesn't put in mu for the velocity, so I am not sure how you calculate that. But once you find the velocity after 1m I figure you'd just check and see if that meets the minimum velocity to spin the object around the pivot.
I could be COMPLETELY wrong however
 
Physics news on Phys.org
i don't think you should use the escape velocity equation (??) to do this. hint: find the gravitational potential energy gained :D
 
Last edited:

Similar threads

Question about springs and rotational/translational energy
  • · Replies 4 ·
Replies
4
Views
2K
Why can we move the spring with constant speed when we apply a force?
  • · Replies 29 ·
Replies
29
Views
3K
Force transmitted to a block in viscous fluid through a spring, cord, and pulley
  • · Replies 6 ·
Replies
6
Views
1K
What Is the Frequency of Small Oscillations for a Pivoted Rod with Two Springs?
  • · Replies 19 ·
Replies
19
Views
2K
An error made in a kinematics question about a spring launcher?
  • · Replies 16 ·
Replies
16
Views
2K
How to solve a differential equation for a mass-spring oscillator?
  • · Replies 2 ·
Replies
2
Views
2K
Projectile Motion : Work and Energy
  • · Replies 4 ·
Replies
4
Views
2K
Help with this problem about a mass oscillating on a spring
  • · Replies 1 ·
Replies
1
Views
1K
Calculating spring constant of a spring loaded cannon
  • · Replies 7 ·
Replies
7
Views
4K
How to find the deceleration of a mass colliding on a spring?
  • · Replies 5 ·
Replies
5
Views
5K