Answer:
a) K = 49.5 J b) k = 1378 N / m c) ΔE = 34 J d) μ = 0.399
Explanation:
For this exercise we will use the concepts of energy
a) The initial kinetic energy is
K = ½ m v²
K = ½ 3.96 5²
K = 49.5 J
b) let's use energy conservation
Em₀ = K = ½ m v²
= Ke = ½ k x²
Em₀ =
½ m v² = ½ k x²
k = m v² / x²
k = 3.96 5² / 0.268²
k = 1378 N / m
c) Let's calculate the final energy of the spring
= Ke = ½ k x²
= ½ 1378 0.15²
= 15.5 J
The initial energy is the kinetics of the block
Em₀ = 49.5 J
The lost energy is the difference with the initial
ΔE = - Em₀
ΔE = 15.5 - 49.5
ΔE = - 34 J
the negative sign means that the energy dissipates
d) For this part we use the concept of work
W = F d cos θ = ΔK
In this case the force is the friction force that always opposes displacement, so the angle 180 ° and cos 180 = -1
W = -fr d = ΔK
The force of friction is
fr = μ N
With Newton's second law
N-w = 0
N = W = mg
Let's calculate
-μ mg d = Kf -K₀o
μ = K₀ / mgd
μ = 49.5 / (3.96 9.8 3.20)
μ = 0.399
Answer:
Explanation:
According to Newton's first law:
The component of the force on the y-axis can be obtained through the Pythagorean Theorem. This is because the components are the cathetus of a right triangle and its hypotenuse is the magnitude of the force:
Replacing and solving for N:
Answer:
The length of a tube and number of rounds are 0.848 m and .
Explanation:
Given that,
Wavelength
m = 160000
We need to calculate the length
Using formula of wavelength
Laser tube behave like closed pipe
Distance traveled by pulse of light in one back and fourth trip
We need to calculate the time
Using formula for time
We need to calculate the number of round
Using formula of number of round
Hence, The length of a tube and number of rounds are 0.848 m and .
Let be the initial velocity of the soccer ball at an angle of inclination of
with the positive x-axis.
Given that:
The horizontal distance covered by the projectile=20 m
Time of flight, seconds
Acceleration due to gravity, downward.
As "north" and "up" as the positive x ‑ and y ‑directions, respectively.
So,
As the acceleration due to gravity is in the vertical direction, so the horizontal component of the initial velocity remains unchanged.
The x-component of the initial velocity, .
The horizontal distance covered by the projectile
m/s
So, the horizontal component of the velocity is 10 m/s which is constant and the graph has been shown in the figure (i).
Now, [as
]
m/s.
The vertical component of the initial velocity,
m/s
Let v be the vertical component of the velocity at any time instant t.
From the equation of motion,
where u: initial velocity, v: final velocity, a: constant acceleration, and t: time taken to change the velocity from u to v.
In this case, we have .
So at any time instant, t.
The vertical component of the velocity, v, is the function of time and related as .
This is a linear equation.
At 2 second, the vertical component of the velocity
v=10-10x2=-10 m/s.
The graph has been shown in figure (ii).
