Answer:
a) k = 2231.40 N/m
b) v = 0.491 m/s
Explanation:
Let k be the spring force constant , x be the compression displacement of the spring and v be the speed of the box.
when the box encounters the spring, all the energy of the box is kinetic energy:
the energy relationship between the box and the spring is given by:
1/2(m)×(v^2) = 1/2(k)×(x^2)
(m)×(v^2) = (k)×(x^2)
a) (m)×(v^2) = (k)×(x^2)
k = [(m)×(v^2)]/(x^2)
k = [(3)×((1.8)^2)]/((6.6×10^-2)^2)
k = 2231.40 N/m
Therefore, the force spring constant is 2231.40 N/m
b) (m)×(v^2) = (k)×(x^2)
v^2 = [(k)(x^2)]/m
v = \sqrt{ [(k)(x^2)]/m}
v = \sqrt{ [(2231.40)((1.8×10^-2)^2)]/(3)}
= 0.491 m/s
We Know, F = m.a
Here, m = 2 Kg
& a = 2 m/s²
Substitute for it,
F = 2*2 Kgm/s²
F = 4 Kgm/s²
This question involves the concepts of general gas equation and pressure.
The force exerted by the gas on one of the walls of the container is "74.08 KN".
First, we will use the general gas equation to find out the pressure of the gas:

where,
P = Pressure of the gas = ?
V = Volume of cube = (side length)³ = (10 cm)³ = (0.1 m)³ = 0.001 m³
n = no. of moles = 3 (since molecules equal to avogadro's number make up 1 mole)
R = general gas constant = 8.314 J/mol.K
T = Absolute Temperature = 24°C + 273 = 297 K
Therefore,

P = 7407.78 KPa
Now, the force on one wall can be given as follows:

where,
A = area of one wall = (side length)² = (0.1 m)² = 0.01 m²
Therefore,

<u>F = 74.08 KN</u>
<u></u>
Learn more about the general gas equation here:
brainly.com/question/24645007?referrer=searchResults
It's always a good idea to wear a seatbelt in a car, because if the car
comes to a sudden stop, you will not move forward very much since the
seatbelt is holding you back. The answer is letter D.