car starts from rest
final speed attained by the car is
acceleration of the car will be
now the time to reach this final speed will be
so it required 1.39 s to reach this final speed
What did johannes kepler contribute to the study of planets? he formulated the universal law of gravitation. he identified the f
1 answer:
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a) The mass is 0.23 kg
b) The spring constant is 1.25 N/m
c) The frequency is 1.42 Hz
d) The speed of the block is 1.08 m/s
Explanation:
a)
We can find the mass of the block by applying the law of conservation of energy: in fact, the total mechanical energy of the system (which is sum of elastic potential energy, PE, and kinetic energy, KE) is constant:
The potential energy is given by
where k is the spring constant and x is the displacement. When the block is crossing the position of equilibrium, x = 0, so all the energy is kinetic energy:
(1)
where
m is the mass of the block
is the maximum speed
We also know that the total energy is
Re-arranging eq.(1), we can find the mass:
b)
The maximum speed in a spring-mass system is also given by
where
k is the spring constant
m is the mass
A is the amplitude
Here we have:
is the maximum speed
m = 0.23 kg is the mass
A = 14.0 cm = 0.14 m is the amplitude
Solving for k, we find the spring constant
c)
The frequency in a spring-mass system is given by
where
k is the spring constant
m is the mass
In this problem, we have:
k = 18.3 N/m is the spring constant (found in part b)
m = 0.23 kg is the mass (found in part a)
Substituting and solving for f, we find the frequency of the system:
d)
We can solve this part by using the law of conservation of energy; in fact, we have
Where v is the speed of the system when the displacement is equal to x.
We know that the total energy of the system is
E = 0.18 J
Also we know that
k = 18.3 N/m is the spring constant
m = 0.23 kg is the mass
Substituting
x = 7.00 cm = 0.07 m
We can solve the equation to find the corresponding speed v:
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