Two iron balls of mass m are connected by a nearly massless spring with spring c

Question

Two iron balls of mass m are connected by a nearly massless spring with spring constant k_s and relaxed length L. A person holding the balls compresses the spring to 1/2 L and then drops the spring-ball assembly from a vertical distance h above the bottom of an insulated bucket containing water of mass M. (Note that because the bucket is an insulator, even if the balls rub against the bucket's walls, the walls will get little thermal energy because thermal energy cannot easily flow into the bucket wall material.) (a) After everything settles down, what is the change in the water's temperature? Express your result in terms of the given symbols and symbols for whatever other quantities you might need. (b) If m = 200 g, k_s = 2000 J/m^2, L = 10 cm, h = 50 cm, and M = 4.0 kg, what is the approximate numerical value of this temperature increase?

Explanation / Answer

(A) initial energy of spring mass system,

E = k ( L / 2)^2 / 2 + (2m)g h

E = K L^2 / 8 + 2 m g h

now this energy will go to water,

E = M C deltaT

deltaT = ( K L^2 /8 + 2 m g h ) / ( M C ) .......Ans

where C = specific heat capacity of water = 4186 J / kg deg C

(B) deltaT = ( ( 2000 x 0.10^2 / 8) + ( 2 x 0.200 x 9.8 x 0.50)) / (4 x 4186)

= 2.66 x 10^-4 deg C

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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