- #1

Fendergutt

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## Homework Statement

A 2.00 kg particle is moved from the coordinates (1.00, 3.00) m to (5.00, 7.00) m.

(q1) How much work is done by the force

**F**= <2x^2, 0> on the particle? (Assume that the force is in Newton when x is in metres.)

(q2) If the particle has start velocity

**v_i**= <0, 4.00 m/s>, what is the final velocity

**v_f**? (Hint: the "work - kinetic energy"-theorem can be useful.)

(q3) Determine the rate of energy transfer (i.e. the effect P) from the force to the particle, at start and final position. (Answers: P_i = 0 W, P_f = 455 W.)

## Homework Equations

## The Attempt at a Solution

(q1) I made a position vector

**AB**= <4, 4>. It takes the particle from (1, 3) to (5, 7). We consider the positional vector's component that is parallell with

**F**.

--> x = 4 m --> W_F = 2 * 4^2 = 32, that is 32 N.

(q2) Start velocity

**v_i**= <0, 4.00 m/s> is constant in y-direction since the only working force on the particle is

**F**, but this force is perpendicular on

**v_i**, and will therefore not alter it.

"Work - kinetic energy"-theorem:

W_total = (delta)K = (1/2)*m(v_F)^2

<--> v_F = sqrt( (2(W_F)) / m ) = sqrt( (2*32 N) / (2 kg) ) = 4sqrt(2) m/s

-->

**v_f**= <v_F, v_i>

--> ||

**v_f**|| = sqrt((v_F)^2 + (v_i)^2) = sqrt( (4sqrt2 m/s)^2 + (4.00 m/s)^2 ) = 4sqrt3 m/s =~ 6.9 m/s

that is in the direction of the vector

**AB**, 45 degrees anticlockwise with the x-axis.

(q3) Effect from force on particle:

at start: P = dW/dt =

**F[/**

*****

ie 0 W

at end: P = dW/dt =

answer: at start: 0 W, at end: 455 W

I must have done something wrong here. I believe the error follows from my try at (q2). Please comment or help me with getting this problem right. Thanks a lot for your time.**v_i**= F * v_i * cos(alpha) = 2*0^2*cos(pi/2) = 0.ie 0 W

at end: P = dW/dt =

**F*****v_f**= F*v_f*cos(theta) = 2* 4^2 * 4sqrt3 * cos(pi/4) W = 64sqrt6 W =~ 157 W.answer: at start: 0 W, at end: 455 W

I must have done something wrong here. I believe the error follows from my try at (q2). Please comment or help me with getting this problem right. Thanks a lot for your time.