A mass oscillating at the end of a spring

AI Thread Summary
A 250-g mass oscillates on a spring with a spring constant of 4.80 N/m and an amplitude of 5.42 cm. The user calculated the acceleration at a displacement of 4.27 cm but made an error in the spring constant, mistakenly using 48 N/m instead of 4.80 N/m. The discussion highlights the need to consider all forces acting on the mass when applying Newton's second law. Additionally, the user seeks clarification on finding the maximum speed of the object and the position at which it occurs. Accurate calculations and understanding of the system's dynamics are essential for solving these problems.
Trinity Nicole
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1. A 250-g object hangs from a spring and oscillates with an amplitude of 5.42 cm. The spring constant is 4.80 N/m.
a) What is the acceleration of the object when the displacement is 4.27 cm [down]?
I put:
m=0.25 kg
d=0.0542 m
k=48 N/m
x=0.0427m
Therefore:
F=kx which leads to a=kx/m
a=(48 N/m)(0.0427 m)/0.25 kg
a=8.10 m/s^2 [up]
b) What is the maximum speed of the object?
I put:
m=0.25 kg
d=0.0542 m
k=48 N/m
x=0.0427m
a=8.10 m/s^2 [up] (I think)
Not sure which equation to use...
c) At what position will the maximum speed occur?
I'd need B to know this, please help me out.
Thanks in advance!
 
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Trinity Nicole said:
k=48 N/m

It looks like you have a typo there -- can you re-check the problem statement? :smile:
 
berkeman said:
It looks like you have a typo there -- can you re-check the problem statement? :smile:
i'm sorry, what is my typo?
 
Trinity Nicole said:
The spring constant is 4.80 N/m.

Trinity Nicole said:
k=48 N/m

:smile:
 
There is another error in the OP solution to a).
In the equation F=ma, F is the net of all forces in the direction of the acceleration. What are all the forces acting on the mass?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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