Answer:
Part a)

Part b)

Explanation:
As the uniform sphere is rolling down the inclined plane then the net force on the sphere is given as

also we have torque equation on it

for pure rolling


now we have

now we have


now given that

so we have



Part b)
If the inclined plane is frictionless then the acceleration is given as



A) initial volume
We can calculate the initial volume of the gas by using the ideal gas law:

where

is the initial pressure of the gas

is the initial volume of the gas

is the number of moles

is the gas constant

is the initial temperature of the gas
By re-arranging this equation, we can find

:

2) Now the gas cools down to a temperature of

while the pressure is kept constant:

, so we can use again the ideal gas law to find the new volume of the gas

3) In a process at constant pressure, the work done by the gas is equal to the product between the pressure and the difference of volume:

by using the data we found at point 1) and 2), we find

where the negative sign means the work is done by the surrounding on the gas.
Answer:
Time, t = 13.34 seconds.
Explanation:
Given the following data;
Initial velocity, u = 85km/hr to meters per seconds = 85*1000/3600 = 23.61 m/s
Final velocity, v = 45km/hr to meters per seconds = 45*1000/3600 = 12.5 m/s
Acceleration, a = -3 km/hr/sec to meters per seconds square = -3*1000/3600 = -0.833m/s²
To find the time;
Acceleration = (v - u)/t
-0.833 = (12.5 - 23.61)/t
-0.833t = -11.11
t = 11.11/0.833
Time, t = 13.34 seconds.
When a satellite is revolving into the orbit around a planet then we can say
net centripetal force on the satellite is due to gravitational attraction force of the planet, so we will have


now we can say that kinetic energy of satellite is given as


also we know that since satellite is in gravitational field of the planet so here it must have some gravitational potential energy in it
so we will have

so we can say that energy from the fuel is converted into kinetic energy and gravitational potential energy of the satellite
The concept required to solve this problem is associated with potential energy. Recall that potential energy is defined as the product between mass, gravity, and change in height. Mathematically it can be described as

Here,
= Change in height
m = mass of super heroine
g = Acceleration due to gravity
The change in height will be,

The final position of the heroin is below the ground level,

The initial height will be the zero point of our system of reference,


Replacing all this values we have,



Since the final position of the heroine is located below the ground, there will net loss of gravitational potential energy of 10744.81J