Answer:
1.10 m/s
Explanation:
Linear speed is given by
Kinetic energy is given by
Potential energy
PE= mgh
From the law of conservation of energy, KE=PE hence
where m is mass, I is moment of inertia,
is angular velocity, g is acceleration due to gravity and h is height
Substituting m2-m1 for m and 0.5l for h,
for
we obtain
and making v the subject
For the rod, moment of inertia
and for sphere
hence substituting 0.5L for R then
For the sphere on the left hand side, moment of inertia I
while for the sphere on right hand side,
The total moment of inertia is therefore given by adding
Substituting
for I in the equation
Then we obtain
This is the expression of linear speed. Substituting values given we get
To solve the problem, we enumerate all the given first. Then the required and lastly the solution.
Given:
V1= 1.56x10^3 L = 1560 L P2 = 44.1 kPa
P1 = 98.9 kPa
Required: V2
Solution:
Assuming the gas is ideal. Ideal gas follows Boyle's Law which states that at a given temperature the product of pressure and volume of a gas is constant. In equation,
PV = k
Applying to the problem, we have
P1*V1 = P2*V2
(98.9 kPa)*(1560 L) = (44.1 kPa)*V2
V2 = 3498.5 L
<em>ANSWER: V2 = 3498.5 L</em>
Answer:
When the temperature of the coffee is 50 °C, the time will be 20.68 mins
Explanation:
Given;
The initial temperature of the coffee T₀ = 95 °C
The temperature of the room = 21°C
Let T be the temperature at time of cooling t in mins
According to Newton's law of cooling;

When the temperature is 50 °C, the time t in min is calculated as;

Therefore, when the temperature of the coffee is 50 °C, the time will be 20.68 mins
= Heat released to cold reservoir
= Heat released to hot reservoir
= maximum amount of work
= temperature of cold reservoir
= temperature of hot reservoir
we know that

eq-1
maximum work is given as
=
- 
using eq-1
=
- 