Calculate Acceleration, Velocity and Force of a Piston

Click For Summary
SUMMARY

The discussion focuses on calculating the acceleration, velocity, and net force of a piston with a mass of 0.25 kg and a stroke length of 9 cm at a rotational speed of 4500 revolutions per minute. The equations used include amax = -w²A for acceleration, vmax = wA for velocity, and Fnetmax = mamax for net force. The discrepancy in answers arises from the misunderstanding of amplitude, where the correct amplitude is 4.5 cm, not 9 cm, as the amplitude is defined as half the stroke length. This clarification resolves the issue of consistently obtaining answers that are half of the expected values.

PREREQUISITES
  • Understanding of basic physics concepts such as acceleration, velocity, and force
  • Familiarity with rotational motion and angular velocity
  • Knowledge of the equations of motion for harmonic oscillators
  • Ability to perform unit conversions, particularly for rotational speed
NEXT STEPS
  • Study the relationship between stroke length and amplitude in oscillatory motion
  • Learn about angular velocity calculations and their applications in mechanical systems
  • Explore the dynamics of harmonic oscillators and their equations of motion
  • Research the impact of mass on acceleration and force in mechanical systems
USEFUL FOR

Students studying physics, mechanical engineers, and anyone interested in understanding the dynamics of pistons and oscillatory motion in mechanical systems.

Pseudopro
Messages
29
Reaction score
0

Homework Statement


Piston mass: 0.25kg
Stroke (distance between extreme positions): 9cm
4500rev min-1

(a)Calculate acceleration of piston at maximum displacement
(b)Calculate velocity as piston moves past its equilibrium point
(c)What is the net force exerted on the piston at maximum displacement

Homework Equations


amax=-w2A
vmax=wA
Fnetmax=mamax

The Attempt at a Solution


(a)amax=-(2\pi4500/60)29\times10-2
(b)similar to (a) using equation
(c)m times answer to (a)

The problem is that the book answer is consistently half my answers. I think this is because they used 4.5cm as their amplitude instead of 9cm. One stroke is 9cm and in one revolution, the piston needs to travel twice that distance, right? So shouldn't amplitude be 9cm?
 
Physics news on Phys.org
The amplitude is half the difference between the high and low.
In a water wave, the water goes up one amplitude, back down to the equilibrium, down one amplitude, then back up to equilibrium.

The piston does the same thing.
 
Thanks, that example makes it clear
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Angular Velocity Problem — a Piston and a Crank
  • · Replies 12 ·
Replies
12
Views
5K
Net force acting on a piston shaft of an actuator
  • · Replies 5 ·
Replies
5
Views
2K
Brake mechanism in a car and pressurised oil
  • · Replies 4 ·
Replies
4
Views
2K
How Does Acceleration Affect Spring Stretch in an Adiabatic Piston System?
  • · Replies 8 ·
Replies
8
Views
3K
Stationary vertical cylinder with heavy piston
  • · Replies 3 ·
Replies
3
Views
3K
Pressure and force in a cylinder
  • · Replies 11 ·
Replies
11
Views
4K
Which one is a correct statement about oscillation?
  • · Replies 24 ·
Replies
24
Views
1K
Finding the Maximum Displacement and Time of a Piston in a Spring-Damper System
  • · Replies 2 ·
Replies
2
Views
1K
Relating acceleration to distance and time
  • · Replies 5 ·
Replies
5
Views
3K
How to Calculate the maximum transvers accleration and velocity
  • · Replies 1 ·
Replies
1
Views
7K