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1. ### Two masses connected by a spring

I talked to my professor and he agrees that the values found in my textbooks are wrong (what I meant before was that my result differs from that of the textbook). Anyway, thank you Alucinator for the tip about the rounding!
2. ### Two masses connected by a spring

Homework Statement Two masses ##m_1=2kg##, ##m_2=2m_1## are placed on the opposite edges of a spring of constant ##k_1=3N/m##, compressed of a length ##x_1=1.73cm##. The system is located on a smooth plane. At the right end of the plane there is a second spring of constant ##k_2=12N/m##. Once...
3. ### Friction of an object on a moving board

So the body exerts a horizontal force F_f on the board in the opposite direction of F? Then Newton's 2nd law for the board is F-F_f=m_Ba_1 and the Newton's law for the body would be: F_f=m_Aa_2?
4. ### Friction of an object on a moving board

On the board: F (and the weight of A which is equilibrated by the board itself). On the body: The force exerted by the board on the body, directed along the direction of F and of a "certain" magnitude and the friction force.
5. ### Friction of an object on a moving board

Homework Statement A body of mass m_A=2 kg is placed on a long board of mass m_B=8 kg at distance d=1 m from the rear edge of the board. The friction coefficient between the body and the board is μ=0.2. A force of magnitude 30 N is applied to the front edge of the board and the body start...
6. ### Interesting convergence of sequence

Homework Statement Let (a_n)_{n\in\mathbb{N}} be a real sequence such that a_0\in(0,1) and a_{n+1}=a_n-a_n^2 Does \lim_{n\rightarrow\infty}na_n exist? If yes, calculate it. Homework Equations The Attempt at a Solution I have a solution but I'd like to see other solutions..
7. ### Maximum power and motion

The maximum power that a train A of mass m can exert when traveling at a velocity v is Pv^{3/2} where P is a constant. The resistance to motion is kv. Why is the equation of motion of A at full power given by: Pv^{1/2}-kv=m\frac{dv}{dt}?