Tut says please help, will rate One end of a spring with a force constant of k =

Question

Tut says please help, will rate

One end of a spring with a force constant of

k = 10.0 N/m

is attached to the end of a long horizontal frictionless track and the other end is attached to a mass

m = 2.20 kg

which glides along the track. After you establish the equilibrium position of the mass-spring system, you move the mass in the negative direction (to the left), compressing the spring 1.98 m. You then release the mass from rest and start your stopwatch, that is

x(t = 0) = ?A,

and the mass executes simple harmonic motion about the equilibrium position. Determine the following.

(a) displacement of the mass (magnitude and direction) 1.0 s after it is released

(b) velocity of the mass (magnitude and direction) 1.0 s after it is released

(c) acceleration of the mass (magnitude and direction) 1.0 s after it is released

(d) force the spring exerts on the mass (magnitude and direction) 1.0 s after it is released

(e) How many times does the object oscillate in 12.0 s? (Do not round your answer to an integer.)
oscillations

Explanation / Answer

(a) Let the acceleration of the system is a m/s^2 and the tension in the string is T newton,By balancing the forces on the two blocks:-
=>T = 4.2a --------------(i)
& 1.1g - T = 1.1a -------(ii)
Thus 1.1 x 9.8 = 5.3a
=>a = 2.03 m/s^2
Same for both the blocks & direction for 1 will be right & direction for 2 will be downward.
(b) BY v = u + at
=>v = 0 + 2.03 x 1
=>v = 2.03 m/s
direction towards right
(c) By s = ut + 1/2at^2
=>s = 0 + 1/2 x 2.03 x (1)^2
=>s = 1.02 m
(d) By s = ut + 1/2at^2
=>s = 0 + 1/2 x 2.03 x (0.35)^2
=>s = 0.12 m
direction for 1:- rightward
direction for 2:- downward

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