Question

The diagram doesnt allow me to paste it here. It is a diagonal line with F1 pointing to the right and F2 pointing the opposite direction. F1=-F2.

Two particles, 1 and 2, with masses m₁ = 8×10^-25 kg and m₂ = 9×10^-25 kg, are constrained to move in the x-y plane. They interact by a repulsive central force, F=k/r₁₂²,
where r₁₂ is the distance between the particles. The diagram shows the situation.

The force on particle 2 is given by
F₂=(k/r₁₂²)
T12
₁₂
where
₁₂=r₁₂/|r₁₂|
is the unit vector in the direction of r₁₂,
r₁₂ = (x₂-x₁)î + (y₂-y₁)ĵ
with the x-y coordinates of the particles,
x_i, y_i, i=1, 2. Note that a unit vector has length 1; its components are numbers and have no units.


Let k= 0.1×10^-25 N· m². Assume the initial components of positions (in meters) and velocities (in m/s) of the particles as given in the table:

x1old	1.30000	vx1old	0.00000
y1old	0.90000	vy1old	0.10000
x2old	-1.40000	vx2old	0.00000
y2old	0.00000	vy2old	-0.80000

Now we will use the ideas of molecular dynamics developed in class to determine how the particles move under the influence of this force. Use 6 sig. figs. in your answers!

20. [1pt]
Calculate the initial distance between the particles, r₁₂.

Correct, computer gets: 2.84605e+00 m

21. [1pt]
Calculate the x component of the unit vector ₁₂.

Correct, computer gets: -9.48683e-01

22. [1pt]
Calculate the y component of ₁₂.

Correct, computer gets: -3.16228e-01

23. [1pt]
Calculate the x component of F₂.

Correct, computer gets: -1.17121e-27 N

24. [1pt]
Calculate the y component of F₂.

Correct, computer gets: -3.90405e-28 N

The force on particle 1 is equal and opposite to the force on particle 2.

25. [1pt]
What is the x component of F₁?

Correct, computer gets: 1.17121e-27 N

The acceleration of particle i is determined by Newton's second law: a_i = F_i/m_i,     i = 1, 2.
One can find the new position and velocity at time t_new = t_old + Δt, where Δt is a small time interval, using

r_i^new = r_i^old + v_i^old Δt + 1/2 ·a_i^old(Δt)²,
v_i^new = v_i^old + a_i^old Δt.
Assume a time step of Δt=0.1 s.

26. [1pt]
Calculate the x component of v₁^new.

Correct, computer gets: 1.46402e-04 m/s

27. [1pt]
Calculate the y component of v₁^new.

Correct, computer gets: 1.00049e-01 m/s

28. [1pt]
Calculate the x component of v₂^new.

Correct, computer gets: -1.30135e-04 m/s

29. [1pt]
Calculate the y component of v₂^new.

Correct, computer gets: -8.00043e-01 m/s

30. [1pt]
Calculate the x component of r₁^new.

Answer:  Last Answer: -0.000276537 m
Not yet correct, tries 3/15

31. [1pt]
Calculate the y component of r₁^new.

Answer:  

32. [1pt]
Calculate the x component of r₂^new.

Answer:  

33. [1pt]
Calculate the y component of r₂^new.