A projectile of mass 0.2 kg and an initial velocity of 50 m/s collides with the end of a blade attached to a turbine. The rotati

Answer:

x₂=2×1

Explanation:

According to the work-energy theorem, we can assume that the gravitational potential energy at the lowest point of compression is zero since the kinetic energy change is 0;

mgx-(kx)²/2 =0 where m refers to the object's mass, g indicates the acceleration due to gravity, k denotes spring constant, and x represents the spring's compression.

mgx=(kx)²/2

x=2mg/k----------------compression when the object is at rest

However, ΔK.E =-1/2mv²⇒kx²=mv² -----------where v symbolizes the object's velocity and K.E signifies kinetic energy

Thus, if kx²=mv² then

v=x *√(k/m) ----------------where v=0

<pDoubling v results in multiplying x *√(k/m) by 2, leading to x₂ being double x₁

Response:

C. vx

F. ax

G. ay

Clarification:

The projectile follows a curved trajectory toward the ground, causing changes in x and y positions.

Since there is no external force acting in the x-direction, the acceleration in x remains at zero. Consequently, ax and vx remain unchanged.

The projectile is subject to the force of gravity, directed downwards, leading to an increase in its velocity due to the rise in its y-component.

Meanwhile, the y-component of acceleration remains constant due to gravitational acceleration.

The heat required to raise the temperature of a substance by is represented by

where m stands for the mass of the substance and indicates the specific heat of the substance. In this situation, we possess and , the specific heat of water.
Consequently, we can ascertain the temperature rise :

Initially, the water's temperature was , so the end temperature should be

Thus, the water is expected to be vapor by now.

However, to give a more accurate statement, during the liquid to vapor transition, the heat added to the system is used to break molecular bonds instead of raising the system's temperature. The heat necessary for the phase change from liquid to vapor is expressed as

where denotes the latent heat of vaporization for water.
Nevertheless, the initial heat input of 50 KJ is less than this requirement, indicating there isn't sufficient heat to finish the liquid-vapor transition. Therefore, the water will remain in the liquid-vapor change phase at a temperature of (the temperature at which the phase change begins)

Answer:

An examination is conducted to assess how basic thin airfoils perform in slightly supersonic flow conditions, utilizing the nonlinear transonic theory initially proposed by von Kármán[1]. Formulas for the pressure coefficient across an oblique shock and a Prandtl-Meyer expansion are devised based on a transonic similarity variable. Aerodynamic coefficients are computed in similarity form for flat plates and asymmetric wedge airfoils, and their graphical representations are created. Sample plots are provided for a flat plate and a particular asymmetric wedge, shown on conventional coordinate axes of Cl, Cd, and Cmc/4 in relation to angle of attack and Cl against Mach Number to showcase distinct characteristics of nonlinear flow.

Explanation: