A mass M = 3 kg that is moving without friction in the xy plane starts at the or

Question

A mass M = 3 kg that is moving without friction in the xy plane starts at the origin (= ~ri) with velocity ~vi = 2^i +^j m/s. Two forces, ~F1 = 2^i + 7^j N and ~F2 = 2^i ?? 5^j N act on the mass as it moves in a straight line to ~rf = 10^i + 5^j m. The power provided by ~F1 at the instant the mass is at ~ri is 1. 5 W 2. 7 W 3. 3 W 4. 0 W 5. None of the above
What is the kinetic energy of the mass when it reaches rf is? 1. 30 J 2. 57.5 J 3. 37.5 J 4. 20 J A mass M = 3 kg that is moving without friction in the xy plane starts at the origin (= ~ri) with velocity ~vi = 2^i +^j m/s. Two forces, ~F1 = 2^i + 7^j N and ~F2 = 2^i ?? 5^j N act on the mass as it moves in a straight line to ~rf = 10^i + 5^j m. The power provided by ~F1 at the instant the mass is at ~ri is 1. 5 W 2. 7 W 3. 3 W 4. 0 W 5. None of the above
What is the kinetic energy of the mass when it reaches rf is? 1. 30 J 2. 57.5 J 3. 37.5 J 4. 20 J What is the kinetic energy of the mass when it reaches rf is? 1. 30 J 2. 57.5 J 3. 37.5 J 4. 20 J

Explanation / Answer

Power= F1.vi=2*2+7*1=11W

F(net)=4i+2j

|F(net)|=sqrt(20)

|rf-ri|=sqrt(125)

F(net) and v(net) are in direction of path

So

Work=sqrt(20)*sqrt(125)=50J=KEf-KEi

So

KEf=50+0.5*3*|vi|^2=57.5J

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