Rosa studies the position-time graph of two race cars. A graph titled Position versus Time shows time in hours on the x axis, nu

Answer:

a)106.48 x 10⁵ kg.m²

b)144.97 x 10⁵ kgm² s⁻¹

Explanation:

a)Given

m = 5500 kg

l = 44 m

The moment of inertia for one blade

= 1/3 x m l²

where m denotes the mass of the blade

l represents the length of each blade.

Substituting the necessary values, the moment of inertia for one blade is

= 1/3 x 5500 x 44²

= 35.49 x 10⁵ kg.m²

Total moment of inertia for 3 blades

= 3 x 35.49 x 10⁵ kg.m²

= 106.48 x 10⁵ kg.m²

b) The angular momentum 'L' is calculated using

L = x ω

where,

= the moment of inertia of the turbine i.e 106.48 x 10⁵ kg.m²

ω= angular velocity =2π f

f represents the frequency of rotation of the blade i.e 13 rpm

f = 13 rpm=>= 13 / 60 revolutions per second

ω = 2π f => 2π  x  13 / 60 rad / s

L= x ω =>106.48 x 10⁵ x   2π  x  13 / 60

  = 144.97 x 10⁵  kgm² s⁻¹    

Details that are not provided: the problem figure is included.

We can address the exercise by applying Poiseuille's law. This law indicates that for a fluid flowing in a laminar manner within a confined pipe,

where:

represents the pressure difference across the two ends

denotes the viscosity of the fluid

L signifies the length of the pipe

indicates the volumetric flow rate, where is the cross-sectional area of the tube and refers to the fluid's velocity

r stands for the pipe's radius.

This law can be utilized for the needle, allowing us to compute the pressure difference between point P and the needle's end. In this scenario, we have:

is the dynamic viscosity of water at

L=4.0 cm=0.04 m

and r=1 mm=0.001 m

Substituting these values into the formula yields:

This pressure difference specifies the value between point P and the needle's termination. As the end of the needle is under atmospheric pressure, the gauge pressure at point P, relative to atmospheric pressure, is exactly 3200 Pa.

Answer:

Induced EMF is 2 x 10⁻³ volts

Explanation:

B = strength of the magnetic field aligning with the loop's axis = 1 T

= area change rate of the loop = 20 cm²/s = 20 x 10⁻⁴ m²

θ = the angle formed by the magnetic field and area vector = 0

E = the induced EMF across the loop

EMF can be calculated using the formula

E = B

E = (1) (20 x 10⁻⁴ )

E = 2 x 10⁻³ volts

E = 2 mV

Response:

Physical well-being

Clarification:

Since you've completed parts a and b, I will tackle part c.
For part C
To respond to this question, we must identify the zeros of the velocity function:

This polynomial can be factored:

Finding the zeros now becomes straightforward since the function equals zero when any factor is zero.

By solving these equations, we identify our zeros:

The particle remains stationary at t=0 and t=3/2.
For part D
We must discover when the velocity function exceeds zero. We will utilize its factored form.
We will assess when each factor is greater than zero and compile the findings in the following table:

From the table, it's evident that our function is positive when and t>3/2.
This indicates the interval during which the particle moves forward.
For part E
The distance traveled can be represented as:

We simply substitute t=12 to calculate the total distance traveled:

For part F
Acceleration is defined as the rate at which velocity changes.
We determine acceleration by deriving the velocity function concerning time.

To find the acceleration at 1 second, we substitute t=1s into the previous equation: