I have a physics midterm on Wednesday and I'm doing some practice problems to prepare. On one of them, I'm getting an answer that is extremely close to the answer my TA gave me for the problem and I can't tell if it's rounding or if I'm missing something.
A mass is attached to a spring and allowed to move horizontally along a surface with friction (assume that the equilibrium position is far enough away from the wall that the mass never hits it and the spring can both push and pull). m=10kg and uK=uS=0.1
If the mass is let go, at x=70 cm (where x=0 is equilibrium) where does it come to rest for the first time?
A) 1/2kx^2=1/2mv^2 -Ff (conservation of energy)
The Attempt at a Solution
-I used equation B to find the frictional force: (0.1)*(9.8)*(10) = 9.8 N
-I used equation C to find the force exerted by the spring: F=(-100)(.7)=-70N. I then used F=ma to get the acceleration: (-70)=(10)a, and a=7m/s^2
I solved equation A for v and got squareroot((kx^2+2f)/m) = v
--after plugging and chugging, i got a velocity v=2.62 m/s
I then plugged into equation D
x=.49 m = 49 cm
The answer my TA gave me was 50.1 cm. Am I doing something incorrectly?
Thanks so much!