**Answer:**

,

**Explanation:**

The problem can be modelled as a vertical mass-spring system exhibiting a simple harmonic motion. The spring constant is:

The angular frequency is:

The frequency and period of oscillations are, respectively:

**Explanation:**

Given data

The elevator mass=3.0×10³ kg

Time t=23 s

elevator lift d=210 m

The power is the average rate of work done:

So

P=F.V Cosα

Where F is force

V is velocity

α is angle between Force and velocity

Apply the Newton Law to find the force on elevator

The velocity of elevator is given as

Since the net force has same direction of motion so α=0°

So

**Answer:**

φ = B sin (2π n/a x)

**Explanation:**

In quantum mechanics when a particle moves freely it implies that the potential is zero (V = 0), so its wave function is

φ = A cos kx + B sin kx

we must place the boundary conditions to determine the value of the constants A and B.

In our case we are told that the particle cannot be outside the boundary given by x = ± a / 2

therefore we must make the cosine part zero, for this the constant A = 0, the wave function remains

φ = B sin kx

the wave vector is

k = 2π /λ

now let's adjust the period, in the border fi = 0 therefore the sine function must be zero

φ (a /2) = 0

0 = A sin (2π/λ a/2)

therefore the sine argument is

2π /λ a/2 = n π

λ= a / n

we substitute

φ = B sin (2π n/a x)

**Answer:**

temperature inside the balloon so it is warmer than the surrounding air

**Explanation:**

For the balloon to get an uplift , it should be lighter than air . That means the density of the gas inside should be less than the density of air outside . only then , weight of the balloon plus the weight of the air inside balloon will become less than the weight of displaced air outside . This can be achieved by warming up the air inside. Its temperature must exceed that of outside air.