Physics & Chemistry Problem Set: Charon Orbit & NiCd Battery

Physics
A Satellite of Pluto
Pluto, a dwarf planet in the outer Solar System, has a natural satellite named Charon.
This satellite, discovered in 1978, has a mass = 1.8 × 10 kg .For simplicity, Charon will be
modeled as a satellite orbiting Pluto. Its trajectory around Pluto is circular; it orbits at an average
= 1.9 × 10 km from Pluto . Its period of revolution is = 6.4 days and its orbital
speed is = 0.2 km.s .
1. Specify the reference frame in which the motion of Charon around Pluto is studied
2. Using Newton’s second law, determine the characteristics of the acceleration vector ⃗of the
center of mass of Charon.
3. Deduce the expression of Charon’s speed as a function of Pluto’s mass and the distance .
Calculate its value. Does it confirm the value given in the text?
4. Express the period of revolution as a function of and .
5. Recover Kepler’s third law. Deduce the value of . Is it consistent with the value given in
the text?
6. Pluto revolves around the Sun with a period = 248years. Determine the average distance
between the center of Pluto and the center of the Sun.
Data: The Earth revolves around the Sun with a period = 1year ;
the average distance (orbital radius) = 1.50 × 10 m.
Mass of Pluto = 1.3 × 10 kg ; Gravitational constant = 6.67 × 10 SI

Chemistry
Nickel–cadmium accumulator
The nickel–cadmium accumulator is very common. Its electromotive force is E= 1.3 V.
The electrolyte is an aqueous potassium hydroxide solution
(potash),containing: ( ), ( )
During discharge, the reactions occurring at the electrodes correspond to the forward direction of
the following equations:
NiO(OH)(s) + H O(l) + e → Ni(OH) (s) + OH (aq)
Cd(s) + 2 OH (aq) → Cd(OH) (s) + 2 e
1. What is the positive terminal of this battery?
2. a) What redox couples are involved in this accumulator?
b) Write the overall operating (discharge) reaction of a nickel–cadmium battery.
c) What is the role of NiO(OH)(s)the nickel oxyhydroxide electrode?
3.
a) To which electrode must the positive terminal of a DC voltage source be connected to
recharge this accumulator?
b) Give the equation of the reaction corresponding to the charging of the accumulator.
4. The accumulator is recharged using a constant current = 2.0 A for 40 min.
a) Calculate the total electric charge delivered to the accumulator.
b) Calculate the mass of he nickel oxyhydroxide NiO(OH)formed during the charging
process.
Data: = 9.65 × 10 C mol ,(Ni) = 58.7 g mol ,
(O) = 16.0 g mol ,(H) = 1.0 g mol )