Explanation:
It is given that,
Focal length of the concave mirror, f = -13.5 cm
Image distance, v = -37.5 cm (in front of mirror)
Let u is the object distance. It can be calculated using the mirror's formula as :
u = -21.09 cm
The magnification of the mirror is given by :
m = -1.77
So, the magnification produced by the mirror is (-1.77). Hence, this is the required solution.
Answer:
(a) The spring constant is 59.23 N/m
(b) The total energy involved in the motion is 0.06 J
Explanation:
Given;
mass, m = 240 g = 0.24 kg
frequency, f = 2.5 Hz
amplitude of the oscillation, A = 4.5 cm = 0.045 m
The angular speed is calculated as;
ω = 2πf
ω = 2 x π x 2.5
ω = 15.71 rad/s
(a) The spring constant is calculated as;
(b) The total energy involved in the motion;
E = ¹/₂kA²
E = (0.5) x (59.23) x (0.045)²
E = 0.06 J
Answer:
The centripetal acceleration as a multiple of is
Explanation:
The centripetal acceleration is defined as:
(1)
Where v is the velocity and r is the radius
Since the person is standing in the Earth surfaces, their velocity will be the same of the Earth. That one can be determined by means of the orbital velocity:
(2)
Where r is the radius and T is the period.
For this case the person is standing at a latitude . Remember that the latitude is given from the equator. The configuration of this system is shown in the image below.
It is necessary to use the radius at the latitude given. That radius can be found by means of trigonometric.
(3)
Where is the radius at the latitude of
and
is the radius at the equator (
).
can be isolated from equation 3:
(4)
Then, equation 2 can be used
Notice that the period is the time that the Earth takes to give a complete revolution (24 hours), this period will be expressed in seconds for a better representation of the velocity.
⇒
Finally, equation 1 can be used:
Hence, the centripetal acceleration is
To given the centripetal acceleration as a multiple of it is gotten:
