How Does a Force Affect the Final Velocity and Momentum of a Moving Body?

[Jtappan]

Homework Statement

A 4 kg body is initially moving northward at 15 m/s. Then a force of 10 N, toward the east, acts on it for a time of 1.9 s.

(a) At the end of that time, what is the body's final velocity? Magnitude ____ m/s
Direction _____ ° north of east

(b) What is the change in momentum during that time?
19.2 5kg·m/s toward the east toward the west

Homework Equations

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The Attempt at a Solution

I got he change in momentum during the time but i don't know how to find the magnitude and direction of the force...

 

[Doc Al]

I got he change in momentum during the time but i don't know how to find the magnitude and direction of the force...

You are given the force and the time. Realize that impulse is a vector quantity.

 

[ogb p]

(a) The final velocity of the body can be found by using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 15 m/s northward, and the acceleration can be found using Newton's second law, F = ma. Since the only force acting on the body is 10 N toward the east, the acceleration will also be toward the east. Therefore, a = F/m = 10/4 = 2.5 m/s². Plugging these values into the equation, we get v = 15 + 2.5(1.9) = 19.75 m/s. This is the magnitude of the final velocity.

To find the direction, we can use trigonometry. The force of 10 N toward the east and the initial velocity of 15 m/s northward form a right angle. Using the Pythagorean theorem, we can find the magnitude of the resultant velocity, which is the hypotenuse of the right triangle formed by these two vectors. This magnitude is √(15² + 19.75²) = 24.84 m/s. To find the direction, we can use the inverse tangent function, tan⁻¹(19.75/15) = 53.13° north of east. Therefore, the final velocity is 19.75 m/s at an angle of 53.13° north of east.

(b) The change in momentum during the time can be found using the equation ∆p = m∆v, where ∆p is the change in momentum, m is the mass, and ∆v is the change in velocity. In this case, the mass is 4 kg and the change in velocity is 19.75 m/s. Therefore, ∆p = 4(19.75) = 79 kg·m/s. This represents the change in momentum toward the east. To find the direction, we can use the same method as in part (a). The force of 10 N toward the east and the change in velocity of 19.75 m/s form a right angle. Using the Pythagorean theorem, we can find the magnitude of the resultant momentum, which is the hypotenuse of the right triangle formed by these two vectors. This magnitude is