Answer:
r = 41.1 10⁹ m
Explanation:
For this exercise we use the equilibrium condition, that is, we look for the point where the forces are equal
∑ F = 0
F (Earth- probe) - F (Mars- probe) = 0
F (Earth- probe) = F (Mars- probe)
Let's use the equation of universal grace, let's measure the distance from the earth, to have a reference system
the distance from Earth to the probe is R (Earth-probe) = r
the distance from Mars to the probe is R (Mars -probe) = D - r
where D is the distance between Earth and Mars
M_earth (D-r)² = M_Mars r²
(D-r) =
r
r (
) = D
r =
We look for the values in tables
D = 54.6 10⁹ m (minimum)
M_earth = 5.98 10²⁴ kg
M_Marte = 6.42 10²³ kg = 0.642 10²⁴ kg
let's calculate
r = 54.6 10⁹ / (1 + √(0.642/5.98) )
r = 41.1 10⁹ m
Answer:
a) 
b) This value of specific heat is close to the specific heat of ice at -40° C and the specific heat of peat (a variety of coal).
c) The material is peat, possibly.
d) The material cannot be ice because ice doesn't exists at a temperature of 100°C.
Explanation:
Given:
- mass of aluminium,

- mass of water,

- initial temperature of the system,

- mass of copper block,

- temperature of copper block,

- mass of the other block,

- temperature of the other block,

- final equilibrium temperature,

We have,
specific heat of aluminium, 
specific heat of copper, 
specific heat of water, 
Using the heat energy conservation equation.
The heat absorbed by the system of the calorie-meter to reach the final temperature.



The heat released by the blocks when dipped into water:

where
specific heat of the unknown material
For the conservation of energy : 
so,


b)
This value of specific heat is close to the specific heat of ice at -40° C and the specific heat of peat (a variety of coal).
c)
The material is peat, possibly.
d)
The material cannot be ice because ice doesn't exists at a temperature of 100°C.
Answer:
a)11.25 J
b)Number of revolution = 1
Explanation:
Given that
Radius ,r= 0.8 m
m= 0.3 kg
Initial speed ,u= 10 m/s
final speed ,v= 5 m/s
a)
Initial energy


KEi= 15 J
Final kinetic energy


KEf=3.75 J
The energy transformed from mechanical to internal = 15 - 3.75 J = 11.25 J
b)
The minimum value to complete the circular arc

Now by putting the values

V= 2.82 m/s
So kinetic energy KE


KE=1.19 J
ΔKE= KEi - KE
ΔKE= 15- 1.19 J
ΔKE=13.80 J
The minimum energy required to complete 2 revolutions = 2 x 11.25 J
= 22.5 J
Here 22.5 J is greater than 13.8 J.So the particle will complete only one revolution.
Number of revolution = 1