Work done by gravity = 23,520 J = mgh. Therefore m= 23520/ 30 x 9.8 = 80 kg.
Answer:
Explanation:
Assuming you mean acceleration is 3 m/s²
s = s₀ + ut + ½at²
d = 0 + 0(35) + ½(3)35² = 1,837.5 m
v = u + at
v = 0 + 3(35) = 105 m/s
Answer:
The diameter of the needle is <u>4.675 cm</u>.
Explanation:
Given:
Volume flow rate is, 
Velocity of air expelled by pump is, 
Let the area of the needle be 'A' cm² and the diameter be 'd' cm.
We know that, volume flow rate of the air expelled by pump is given as the product of the needle's area and velocity of air flowing through that area.
Therefore, volume flow rate is given as:

Now, considering the needle to be circular, area of the needle can be written as:

Therefore, the diameter of the needle is 4.675 cm.
Answer:
30 m³
Explanation:
Parameters given:
Initial volume of helium, V1 = 5 m³
Initial pressure in balloon, P1 = 30 kPa
Final pressure, P2 = 5 kPa
To find the volume of the balloon at that volume, we apply Boyle's law.
It states that at constant temperature, the pressure of a gas is inversely proportional to the volume of the gas.
Mathematically:
P = k / V
Where k = constant of proportionality
This implies that:
P * V = k
This means that if the pressure or volume of the gas changes at the same temperature, the product of the pressure and volume would be the same:
Hence:
P1 * V1 = P2 * V2
Hence, to find the final volume:
30 * 5 = 5 * V2
=> V2 = (30 * 5) / 5
V2 = 30 m³
The volume of the gas when the pressure is 5 kPa is 30 m³.
Answer:
The price per kWh is 
The energy density in watt-hours per lb is 
Explanation:
From the question we are told that
The voltage of the battery is 
The capacity of the battery is 
The price is 
The weight of the battery is 
Generally the energy generated by the battery is mathematically represented as

Here P is power which is represented as

So

=> 
=> 
=> 
converting to kW h
=>
=>
Generally the cost of this energy produced is
Hence the cost of 1 kWh is mathematically represented as

=> 
=> 
Generally the energy density is mathematically represented as

=> 
=> 