How Do You Calculate Work and Power for a Moving Object?

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SUMMARY

The discussion focuses on calculating work and power for a moving object subjected to a force vector of F = (5.10 N)i + (9.50 N)j + (7.50 N)k. The object, with a mass of 2.30 kg, moves from an initial position vector A = (1.30 m)i - (9.70 m)j + (7.90 m)k to a final position vector B = -(1.90 m)i + (4.80 m)j + (8.00 m)k over a time interval of 4.50 seconds. The work done is determined using the dot product of the force and displacement vectors, while average power is calculated by dividing work by time. The angle between the initial and final position vectors is also a key calculation.

PREREQUISITES
  • Understanding of vector notation and operations
  • Knowledge of Newton's second law (F = ma)
  • Familiarity with the dot product of vectors
  • Basic concepts of work (W = F · d) and power
NEXT STEPS
  • Calculate the displacement vector d = B - A
  • Perform the dot product to find work done (W = F · d)
  • Determine average power using the formula P = W/t
  • Calculate the angle between vectors A and B using the cosine rule
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators looking for problem-solving strategies in work and power calculations.

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Homework Statement



A force = (5.10 N) + (9.50 N) + (7.50 N) acts on a 2.30 kg mobile object that moves from an initial position of i = (1.30 m) - (9.70 m) + (7.90 m) to a final position of f = -(1.90 m) + (4.80 m) + (8.00 m) in 4.50 s. Find (a) the work done on the object by the force in the 4.50 s interval, (b) the average power due to the force during that interval, and (c) the angle between vectors i and f.

Homework Equations



W= F dot d

W= F*d

The Attempt at a Solution



First I attempted to solve for a by doing the dot product of the force vector and the d final but that didn't work. Then I found the magnitudes of F and d final and multiplied them but then that didn't work either. Am I supposed to use F= ma and find the acceleration? but if its that what am I supposed to find after?

Homework Statement


Homework Equations


The Attempt at a Solution

Solved
 
Last edited:
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danest said:

Homework Statement



A force = (5.10 N) + (9.50 N) + (7.50 N) acts on a 2.30 kg mobile object that moves from an initial position of i = (1.30 m) - (9.70 m) + (7.90 m) to a final position of f = -(1.90 m) + (4.80 m) + (8.00 m) in 4.50 s. Find (a) the work done on the object by the force in the 4.50 s interval, (b) the average power due to the force during that interval, and (c) the angle between vectors i and f.
You better write the problem in the proper vector form. Like
F = (5.10 N)i + (9.50 N)j + (7.50 N)k
Initial position vector A = (1.30 m)i - (9.70 m)j + (7.90 m)k
Final position vector B = -(1.90 m)i + (4.80 m)j + (8.00 m)k
The displacement vector d = (B - A)
Now find w = F.d
 

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