Answer:

The spring constant required = 949.2 N/m

Explanation:

The energy stored in the spring is converted to kinetic energy of the projectiles fired.

Energy stored in spring's = kx²/2

Kinetic energy of bullets = mv²/2

k = spring constant = ?

x = maximum compression of the spring = 8 cm = 0.08 m

m = mass of projectiles fired = 3.0 g = 0.003 kg

v = velocity of projectiles fired = 45.0 m/s

kx² = mv²

k (0.08²) = 0.003 (45²) = 6.075

k = 949.2 N/m

The spring constant required = 949.2 N/m

**Answer:**

Specific heat capacity, c = 468.75 J/Kg°C

**Explanation:**

Given the following data;

Power = 1.5 kW to Watts = 1.5 * 1000 = 1500 Watts

Time = 5 seconds

Mass = 0.2 kg

Initial temperature = 20°C

Final temperature = 100°C

To find specific heat capacity;

First of all, we would have to determine the energy consumption of the kettle;

Energy = power * time

Energy = 1500 * 5

Energy = 7500 Joules

Next, we would calculate the specific heat capacity of water.

Heat capacity is given by the formula;

Where;

- Q represents the heat capacity or quantity of heat.
- m represents the mass of an object.
- c represents the specific heat capacity of water.
- dt represents the change in temperature.

dt = T2 - T1

dt = 100 - 20

dt = 80°C

Making c the subject of formula, we have;

Substituting into the equation, we have;

<em>**Specific heat capacity, c = 468.75 J/Kg°C**</em>

**Answer:**

**The resistance of the first resistor is, R₁ = 10 Ω**

**Explanation:**

Given data,

The potential of the cell v = 3 V

The current through the first resistor, I = 0.2 A

The P.D across the first resistor, v₁ = 2.0 V

Let R₁, and R₂ be the resistance of the resistors,

Since the voltage across the series connection is,

v = v₁ + v₂

Substituting the values

3 V = 2 V + v₂

∴ v₂ = 1 V

**Hence, the P.D across the second resistor is, v₂ = 1 V**

The resistance of the first resistor is,

R₁ = v₁ / I

= 2 V / 0.2 A

= 10 Ω

**Hence, the resistance of the first resistor is, R₁ = 10 Ω**

According to the trichromatic theory of color vision, also known as the Young-Helmholtz theory of color vision, there are three receptors in the retina that are responsible for the perception of color. One receptor is sensitive to the color green, another to the color blue and a third to the color red.

Hope this helps.