To solve this we are going to use the formula for ideal mechanical advantage:
where
is the machine mechanical advantage
is the input distance
is the output distance
We know for our problem that
and
. Lets replace those values in our formula to find
:
The ideal machine advantage of the machine is 3. The inventor is claiming that the actual mechanical advantage of the machine is 4. Since the actual mechanical advantage takes into account energy losses, it is always less than the ideal mechanical advantage.
We can conclude that the developer's claim is false.
Answer:
The critical angle is
Explanation:
Snell's law is mathematically represented as
Where is the refractive index of medium 1
is the refractive index of medium 2
Now substituting for and ac which denotes the critical angle for
Making ac the subject
From the question we are told that
The is implies that ac < 90
since
Critical angle is that angle of incidence that result to a 90 degree angle of refraction
Answer:
k = 1073.09 N/m
A = 0.05 m
Explanation:
Given:
- Time period T = 0.147 s
- maximum speed V_max = 2 m/s
- mass of the block m = 0.67 kg
Find:
- The spring constant k
- The amplitude of the motion A.
Solution:
- A general simple harmonic motion is modeled by:
x (t) = A*sin(w*t)
- The velocity of the above modeled SHM is:
v = dx / dt
v(t) = A*w*cos(w*t)
- Where A is the amplitude in meters, w is the angular speed rad/s and time t is in seconds.
- We can see that maximum velocity occurs when (cos(w*t)) maximizes i.e it is equal to 1 or -1. Hence,
- V_max = A*w
- Where w is related to mass of the object and spring constant k as follows,
w = sqrt ( k / m )
- The relationship between w angular speed and Time period T is:
w = 2*pi / T
- Equating the above two equations we have,
m*(2*pi / T)^2 = k
- Hence, k = 0.67*(2*pi / 0.157)^2
k = 1073.09 N / m
- So, amplitude A is:
A = V_max*sqrt ( m / k )
A = 2*sqrt ( 0.67 / 1073.09 )
A = 0.05 m
Answer:
(a) λ = 0.1224 m
(b) λ = 12500 m = 12.5 km
Explanation:
The wavelength can be calculated with the help of the frequency of the waves. The formula utilized for this purpose is given as follows:
where,
c = speed of light = 3 x 10⁸ m/s
λ = wavelength of the wave
f = frequency of the wave
(a)
f = 2.45 GHz = 2.45 x 10⁹ Hz
λ = ?
Therefore,
<u>λ = 0.1224 m</u>
<u></u>
(b)
f = 24 KHz = 2.45 x 10³ Hz
λ = ?
Therefore,
<u>λ = 12500 m = 12.5 km</u>
They attract each other with force
F=q1*q2/(4πεr^2), where
q1=2.4 µC, q2=4.2 µC,
r=4.9·10-2 m, ε=8.854·10^(-12) SI units.
♦ F=2.4·10-6 * 4.2·10-6 /(4*pi* 8.854·10^(-12) *0.049^2)=
=37.73 N;