There are (one can say) three coequal theories of motion for a single particle: Newton's second law, stating that the total force on an object causes its acceleration; the work-kinetic energy theorem, stating that the total work on an object causes its change in kinetic energy; and the impulse-momentum theorem, stating that the total impulse on an object causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A 4.00-kg object has velocity 7.00ĵ m/s. Then, a constant net force 11.0î N acts on the object for 4.50 s. a) Calculate the object's final velocity, using the impulse-momentum theorem. vf = m/s

Question

Branson Manning

Physics

15 September, 11:56

There are (one can say) three coequal theories of motion for a single particle: Newton's second law, stating that the total force on an object causes its acceleration; the work-kinetic energy theorem, stating that the total work on an object causes its change in kinetic energy; and the impulse-momentum theorem, stating that the total impulse on an object causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A 4.00-kg object has velocity 7.00ĵ m/s. Then, a constant net force 11.0î N acts on the object for 4.50 s. a) Calculate the object's final velocity, using the impulse-momentum theorem. vf = m/s

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Aylin Case · Answer 1

vf = 14.2176 m/s

Explanation:

Given

m = 4 Kg

viy = 7.00 ĵ m/s

Fx = 11.0 î N

t = 4.5 s

vf = ?

Using the Impulse - Momentum Theorem, we have

F*Δt = m*Δv ⇒ F*Δt = m * (vf - vi)

⇒ vf = (F*Δt + m*vi) / m

⇒ vf = (F*Δt + m*vi) / m

For x-component

⇒ vfx = (Fx*Δt + m*vix) / m = (11 N*4.5 s + 4 Kg*0 m/s) / (4 Kg)

⇒ vfx = 12.375 î m/s

For y-component

⇒ vfy = (Fy*Δt + m*viy) / m = (0 N*4.5 s + 4 Kg*7 m/s) / (4 Kg)

⇒ vfy = 7 ĵ m/s

Finally:

vf = √ (vfx² + vfy²)

⇒ vf = √ ((12.375 m/s) ² + (7 m/s) ²)

⇒ vf = 14.2176 m/s