Sobre un cuerpo de 700 g de masa que se apoya en una mesa horizontal se aplica una fuerza de 5N en la dirección del plano. Calcu
1 answer:
Answer:
(a) Ff = 3.95N
(b) Ff = 5N
Explanation:
(a) To find the friction force you use the second Newton law:
But you take into account the applied force and the opposite friction force:
you do Ff the subject of the formula and replace the values of the parameters:
(b) In the case of a motion with constant velocity you have that there is no acceleration. Hence:
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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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