Answer:
a) k= 3232.30 N / m, b) f = 4,410 Hz
Explanation:
In this exercise, the car + spring system is oscillating in the form of a simple harmonic motion, as the four springs are in parallel, the force is the sum of the 4 Hocke forces.
The expression for the angular velocity is
w = √k/m
the angular velocity is related to the period
w = 2π / T
we substitute
T = 2
√m/ k
a) empty car
k = 4π² m / T²
k = 4 π² 1310/2 2
k = 12929.18 N / m
This is the equivalent constant of the short springs
F1 + F2 + F3 + F4 = k_eq x
k x + kx + kx + kx = k_eq x
k_eq = 4 k
k = k_eq / 4
k = 12 929.18 / 4
k= 3232.30 N / m
b) the frequency of oscillation when carrying four passengers.
In this case the plus is the mass of the vehicle plus the masses of the passengers
m_total = 1360 + 4 70
m_total = 1640 kg
angular velocity and frequency are related
w = 2pi f
we substitute
2 pi f = Ra K / m
in this case the spring constant changes us
k_eq = 12929.18 N / m
f = 1 / 2π √ 12929.18 / 1640
f = π / 2 2.80778
f = 4,410 Hz
The image height is -10 cm (the image is upside down)
Explanation:
We can solve the problem by using the mirror equation:
where:
f = 5 cm is the focal length of the mirror
p = 10 cm is the distance of the object from the mirror
q is the distance of the image from the mirror
Solving for q, we find:
So, the distance of the image from the mirror is 10 cm.
Now we can find the image height by using the magnification equation:
where
y' is the height of the image
y = 1 cm is the height of the object
and using
p = 10 cm
q = 10 cm
We find the size of the image:
where the negative sign indicates that the image is upside down.
#LearnwithBrainly
Answer:
See explanations below
Explanation:
According to Newtons second law of motion
F = mass * acceleration
F = ma
If mass of an object is decreased to half, then m₂ = 1/2 m
If acting force is reduced by quarter, then F₂ = 3/4 F
F₂ = m₂a₂
3/4F = 1/2m a₂
Divide both expressions
(3/4F)/F = (1/2m)a₂/ma
3/4 = 1/2a₂/a
3/4 = a₂/2a
4a₂ = 6a
2a₂ = 3a
a₂ = 3/2 a
Hence the acceleration of its motion will be one and a half of its original acceleration.
