Finding work done on object with a chnaging force

Click For Summary
SUMMARY

The discussion focuses on calculating the work done on a 5.0 kg particle-like object subjected to a force, with its position defined by the equation x = 3.0t - 4.0t² + 1.0t³. The user initially derived the velocity function v = 3 - 8t + 3t² and attempted to calculate work using W = 0.5m(v² - v₀²), arriving at an incorrect result of 20 Joules. The error lies in the application of the work-energy principle, particularly in the correct evaluation of the velocity at the specified time intervals and the signs involved in the calculations.

PREREQUISITES
  • Understanding of kinematics and motion equations
  • Familiarity with calculus, specifically differentiation
  • Knowledge of the work-energy theorem
  • Basic physics concepts related to force and mass
NEXT STEPS
  • Review the work-energy theorem and its applications in physics
  • Practice deriving velocity and acceleration from position functions
  • Explore the implications of sign conventions in physics calculations
  • Learn about integrating force over a distance to find work done
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and the work-energy principle, as well as educators looking for examples of common calculation errors in kinematics.

emilykorth
Messages
13
Reaction score
0

Homework Statement



A single force acts on a 5.0 kg particle-like object in such a way that the position of the object as a function of time is given by x = 3.0t - 4.0t ^2 + 1.0t ^3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 2.0 s.



Homework Equations



W=Fd

The Attempt at a Solution


I started by finding the derivative of x = 3.0t - 4.0t ^2 + 1.0t ^3 which would be the velovity of the particle like object. (v=3-8t+3t^2)Then I plugged in 0 for when time=0 to find the velocity and then plugged in 2 for t to find the velocity when t=2 seconds. I then used the equation W=.5m(v^2-vo^2) to find that W=20 Joules however this was wrong
What am I doing wrong?
 
Physics news on Phys.org
Be careful with signs.
 

Similar threads

Solving for Work Done When Accelerating a Mass
  • · Replies 3 ·
Replies
3
Views
1K
Work done by a force down a ramp
  • · Replies 11 ·
Replies
11
Views
2K
How do I find the work done for a 100 N downward force?
  • · Replies 4 ·
Replies
4
Views
2K
My Mistake? Understanding Friction Force & Work Done on Snowy & Icy Surfaces
  • · Replies 29 ·
Replies
29
Views
3K
Finding the work done by a block
  • · Replies 4 ·
Replies
4
Views
3K
Work done on moving a submerged object
  • · Replies 3 ·
Replies
3
Views
2K
Work done on crate moving on incline
  • · Replies 28 ·
Replies
28
Views
2K
Spring constant formlula for Force and Work Done
  • · Replies 12 ·
Replies
12
Views
2K
Resistance force changing the velocity of an object
  • · Replies 8 ·
Replies
8
Views
1K
Work Done in slowly pulling a thread
  • · Replies 28 ·
Replies
28
Views
2K