**Answer:**

8.9

**Explanation:**

We can start by calculating the initial elastic potential energy of the spring. This is given by:

(1)

where

k = 35.0 N/m is the initial spring constant

x = 0.375 m is the compression of the spring

Solving the equation,

Later, the professor told the student that he needs an elastic potential energy of

U' = 22.0 J

to achieve his goal. Assuming that the compression of the spring will remain the same, this means that we can calculate the new spring constant that is needed to achieve this energy, by solving eq.(1) for k:

Therefore, Tom needs to increase the spring constant by a factor:

**Answer:**

<h3>30.405°C</h3>

**Explanation:**

Using the formula for heart capacity;

Q = mcΔt

m is the mass = 150g = 0.15kg

initial temperature = 22°C

Quantity of heat = 3240J = 3.24kJ

specific heat capacity of ethanol = 2.57 [kJ/kg K]

Substitute and get the final temperature

3.240 = 0.15(2.57)(T - 22)

3.240 = 0.3855(T-22)

3.240/0.3855 = T - 22

8.405 = T - 22

T = 22+8.405

T = 30.405°C

**Hence the final temperature of the ethanol if 3240 J was needed to raise the temperature of the ethanol is 30.405°C**

**Answer:**

Req = 50 Ω

**Explanation:**

The equivalent resistance is basically the sum of all the resistances in a circuit.

The sum of these resistances will depend whether these resistance are in series or parallel.

If the resistances are on series, the expression to use is:

**R = R₁ + R₂ + R₃ + .......Rₙ (1)**

If the resistances are on parallel then the expression to use is:

**1/R = 1/R₁ + 1/R₂ + ........1/Rₙ (2)**

Now, according to the picture, we have R₁ and R₄ in series, so here we have to use (1):

R₁₄ = 10 + 30 = 40 Ω

R₂ and R₃ are in parallel so we use (2):

1/R₂₃ = 1/20 + 1/20 = 2/20 = 1/10

R₂₃ = 10 Ω

Finally, R₁₄ and R₂₃ are in series (Because of the sum of the resistance in each side, they are now forming one resistance in each side), therefore, we use (1) again to get the equivalent resistance of the whole circuit:

Req = 10 + 40

<h2>

**Req = 50 Ω**</h2>

Hope this helps

**Answer:**

B

**Explanation:**

Because the main focus of cognitive psychology is on the metal processes that affect behavior

**Answer: **D(t) =

**Explanation: **A harmonic motion of a spring can be modeled by a sinusoidal function, which, in general, is of the form:

y = or y =

where:

|a| is initil displacement

is period

For a Damped Harmonic Motion, i.e., when the spring doesn't bounce up and down forever, equations for displacement is:

or

For this question in particular, initial displacement is maximum at 8cm, so it is used the cosine function:

period =

12 =

ω =

Replacing values:

The equation of displacement, D(t), of a spring with damping factor is .