String with masses on either end being pulled from the center

[CSPhysics]

Homework Statement

Two equal 1 kg masses are connected by a light 1.6 m string on a flat frictionless surface. A 2 N force is applied to the midpoint of the string which causes the system to accelerate in the positive x-direction.

After 1.5 seconds, the rope makes an angle of 55° with the x-axis.

Determine:
a) The change in the location of the center of mass at time t = 1.5 s
b) The kinetic energy associated with the center of mass motion
c) The work done by the force from time t = 0 to t = 1.5

Homework Equations

W = Fd
Δp = mΔv = Ft
K = 0.5mv²

The Attempt at a Solution

I started with part b and solved for the center of mass velocity.
Ft = mv
v(t) = Ft/m
v(1.5) = (2)(1.5)/2 = 1.5 m/s
K = 2.25 JThen for part a, I integrated my velocity function to get
x(t) = Ft²/2m
x(1.5) = 1.125

For part c, I calculated force displacement to get work
force displacement = 1.125 + 0.8sin(55) = 1.78 m
W = Fd
W = 2 * 1.78
W = 3.56 J

I have no idea if what I did is correct, and I haven't been able to find any similar questions online. Any help is appreciated!

 

[haruspex]

Ft = mv
v(t) = Ft/m
v(1.5) = (2)(1.5)/2 = 1.5 m/s
K = 2.25 J

Force, velocity and momentum are vectors, KE is not. Think about directions. What have you overlooked?

 

[CSPhysics]

Force, velocity and momentum are vectors, KE is not. Think about directions. What have you overlooked?

I'm thinking of it in terms of a force acting on the entire system and changing its momentum. The force is along the x-axis so the velocity should also be along that axis.

If I needed to calculate the total KE then I would need to consider the y-component of the masses' motion but if I understand it correctly, that should not effect the motion of the center of mass and the KE associated with that motion.

 

[haruspex]

I'm thinking of it in terms of a force acting on the entire system and changing its momentum. The force is along the x-axis so the velocity should also be along that axis.

If I needed to calculate the total KE then I would need to consider the y-component of the masses' motion but if I understand it correctly, that should not effect the motion of the center of mass and the KE associated with that motion.

Sorry, you are right. I did not think carefully about what the question was asking.

0.8sin(55)

Cos maybe?

 

[CSPhysics]

Sorry, you are right. I did not think carefully about what the question was asking.Cos maybe?

No worries!

Yes, that should definitely be cos, Aside from that, does everything else I did see to make sense?

 

[haruspex]

No worries!

Yes, that should definitely be cos, Aside from that, does everything else I did see to make sense?

Yes.