A spring of negligible mass has one endattached to the ceiling. When a mass of M

Question

A spring of negligible mass has one endattached to the ceiling. When a mass of M=1.5 kg is attached to theother end of the spring and lowered slowly, the spring stretches adistance of R=0.020 m, so thatthe top of the mass M is initially stationary at a position ofy(0)=-0.30 m as measured from the ceiling. A small clay ball ofmass m=0.25 kg is dropped from the ceiling onto the top of the massM, so that the clay sticks to the mass M at timet=0.

a) What is the spring constant of thespring?

735 N/m

b) Find the speed of clay ball justbefore it hits the mass M.

2.42 m/s

c) Find the speed of the mass Mimmediately after the clay sticks to it.

d) Find the period for oscillations ofthe spring.

e) Given that the position of the massas a function of time is y(t)=y(0)!y0cos(t+),find the values for the amplitude (y0) and phase()of the oscillations.

Explanation / Answer

you can find the speed immediately after impact using conservationof momentum mv = (M+m)v1.25kg * 2.42m/s = 1.75kg * v1 v = .3457m/s we know that Vmax = A = 2f = 2 / T Vmax = 2 A / T T = 2 A / Vmax but we don't know A.... yet conservation of energy tells us that 1/2 k A2 = 1/2 mVmax2 A2 = m Vmax2 / k A = (1.75 * .34572 / 735) A = .0169m T = 2 A / Vmax T = 2 * * .0169 / .3457 = .307sec message me if you need any more help after this part

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.