There are (one can say) three coequal theories of motion: Newton\'ssecond law, s
ID: 1722790 • Letter: T
Question
There are (one can say) three coequal theories of motion: Newton'ssecond law, stating that the total force on an object causes itsacceleration; the work-kinetic energy theorem, stating that thetotal work on an object causes its change in kinetic energy; andthe impulse-momentum theorem, stating that the total impulse on anobject causes its change in momentum. In this problem, you comparepredictions of the three theories in one particular case. A2.50 kg object has velocity 7.00j m/s.Then, a total force 13.0i N acts onthe object for 5.00 s. (a) Calculate the object's final velocity,using the impulse-momentum theorem.1i m/s + 2jm/s
(b) Calculate its acceleration from a = (vf- v0)/t.
3i m/s2
(c) Calculate its acceleration from a = f/m.
4i m/s2
(d) Find the object's vector displacement from r =v0t + 1/2 at2.
5i m + 6jm
(e) Find the work done on the object from W =F·r.
7 J
(f) Find the final kinetic energy from 1/2mvf2 = 1/2 mvf·vf .
8 J
(g) Find the final kinetic energy from 1/2mv02 + W.
9 J
(h) State the result of comparing the answers to parts (b) and (c),and the answers to parts (f) and (g). (a) Calculate the object's final velocity,using the impulse-momentum theorem.
1i m/s + 2jm/s
(b) Calculate its acceleration from a = (vf- v0)/t.
3i m/s2
(c) Calculate its acceleration from a = f/m.
4i m/s2
(d) Find the object's vector displacement from r =v0t + 1/2 at2.
5i m + 6jm
(e) Find the work done on the object from W =F·r.
7 J
(f) Find the final kinetic energy from 1/2mvf2 = 1/2 mvf·vf .
8 J
(g) Find the final kinetic energy from 1/2mv02 + W.
9 J
(h) State the result of comparing the answers to parts (b) and (c),and the answers to parts (f) and (g).
Explanation / Answer
. Mass (m) = 2.50 kg ; Initialvelocity (v1 ) = 7.00 j ; Force (F) = 13.0 i ; time (t) = 5.00 s . (a) We know that : . F * t = m (v2 - v1 ) . ( 13.0 * 5.00) i = 2.50 ( v2 - 7.00 j) . 26 i = ( v2 - 7.00 j ) . or v2 = 26 i + 7.00 j . (b) Acceleration is : . a = ( v2 - v1 ) / t = ( 26 i + 7.00 j - 7.00 j ) / 5.00 = 5.2 i . (c) Acceleration : . a = f / m = 13.0 i / 2.50 = 5.2 i . (d) Displacement is : . r = v1t + 1/2a t2 = 7.00 j * 5.00 + (0.5 * 5.2 i * 25 ) = 65 i + 35 j . (e) Work done is : . W = 13.0 i . ( 65 i + 35 j) = 845 J . (f) Final kinetic energy : 0.5 * 2.50 kg * ( sqrt [ ( 26 )2 + (7.00)2 ] )2 . = 906.25 J . (g) Kinetic energy is : . 1/2 mv02 + W = 906.25 J . (f) Answers in (b) and (c) are equal ; similarly (f) and (g) areequal. . Hope thishelps u!Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.