To solve this problem it is necessary to apply the concepts related to Hooke's Law as well as Newton's second law.
By definition we know that Newton's second law is defined as
m = mass
a = Acceleration
By Hooke's law force is described as
Here,
k = Gravitational constant
x = Displacement
To develop this problem it is necessary to consider the two cases that give us concerning the elongation of the body.
The force to keep in balance must be preserved, so the force by the weight stipulated in Newton's second law and the force by Hooke's elongation are equal, so
So for state 1 we have that with 0.2kg there is an elongation of 9.5cm
For state 2 we have that with 1Kg there is an elongation of 12cm
We have two equations with two unknowns therefore solving for both,
In this way converting the units,
Therefore the spring constant is 313.6N/m
C. Combustion reaction.
These reaction are exothermic.
The reactions are:
2Mg + O2 -----> 2MgO
3Mg + N2 ------> Mg3N2
Answer:
Radio waves have the longest wavelengths in the EM spectrum, according to NASA, ranging from about 0.04 inches (1 millimeter) to more than 62 miles (100 kilometers).
Band Frequency range Wavelength range
Very Low Frequency (VLF) 3 to 30 kHz 10 to 100 km
Low Frequency (LF) 30 to 300 kHz 1 m to 10 km
Explanation:
To solve this problem we will apply the principle of conservation of energy, for which the initial potential and kinetic energy must be equal to the final one. The final kinetic energy will be transformed into rotational and translational energy, so the mathematical expression that approximates this deduction is
KE_i+PE_i = KE_{trans}+KE_{rot} +PE_f
, since initially cylinder was at rest
since at the ground potential energy is zero
The mathematical values are,
Here,
m = mass
g= Gravity
h = Height
V = Velocity
moment of Inertia in terms of its mass and radius
Angular velocity in terms of tangential velocity and its radius
Replacing the values we have that
mgh = \frac{1}{2} mv^2 +\frac{1}{2} (\frac{mr^2}{2})(\frac{v}{r})^2
gh = \frac{v^2}{2}+\frac{v^2}{4}
v = \sqrt{\frac{4gh}{3}}
From trigonometry the vertical height of inclined plane is the length of this plane for 
, then
Replacing,
Therefore the cylinder's speedat the bottom of the ramp is 3.32m/s
Answer:
Horizontal component = 241 N
Vertical component = 287 N
Explanation:
Given:
Force = F = 375 N
Referring to diagram attached, the force F is making an angle
theta = 20+30 = 50 with the horizontal.
Horizontal component = F*cos(theta) = 375*0.64278 = 241 N
Vertical component = F*sin(theta) = 375*0.76604 = 287 N
