Answer:
v_g,i = 1.208 m/s
Explanation:
We are given;
Mass of girl; m_g = 47.2 kg
Mass of plank; m_p = 177 kg
Let the velocity of girl to ice be v_g,i
Let the velocity of plank to ice be v_p,i
Since the velocity of the girl is 1.53 m/s relative to the plank, then;
v_g,i + v_p,i = 1.53
From conservation of momentum;
m_g × v_g,i = m_p × v_p,i
Thus;
47.2(v_g,i) = 177(v_p,i)
Dividing both sides by 47.2 gives;
v_g,i = 3.75(v_p,i)
v_pi = (v_g,i)/3.75
Thus, from v_g,i + v_p,i = 1.53, we have;
v_g,i + ((v_g,i)/3.75) = 1.53
v_g,i(1 + 1/3.75) = 1.53
1.267v_g,i = 1.53
v_g,i = 1.53/1.267
v_g,i = 1.208 m/s
Energy flows with kinetic energy
Answer:
a) k = 120 N / m
, b) f = 0.851 Hz
, c) v = 1,069 m / s
, d) x = 0
, e) a = 5.71 m / s²
, f) x = 0.200 m
, g) Em = 2.4 J
, h) v = -1.01 m / s
Explanation:
a) Hooke's law is
F = k x
k = F / x
k = 24.0 / 0.200
k = 120 N / m
b) the angular velocity of the simple harmonic movement is
w = √ k / m
w = √ (120 / 4.2)
w = 5,345 rad / s
Angular velocity and frequency are related.
w = 2π f
f = w / 2π
f = 5.345 / 2π
f = 0.851 Hz
c) the equation that describes the movement is
x = A cos (wt + Ф)
As the body is released without initial velocity, Ф = 0
x = 0.2 cos wt
Speed is
v = dx / dt
v = -A w sin wt
The speed is maximum for sin wt = ±1
v = A w
v = 0.200 5.345
v = 1,069 m / s
d) when the function sin wt = -1 the function cos wt = 0, whereby the position for maximum speed is
x = A cos wt = 0
x = 0
e) the acceleration is
a = d²x / dt² = dv / dt
a = - Aw² cos wt
The acceleration is maximum when cos wt = ± 1
a = A w²
a = 0.2 5.345
a = 5.71 m / s²
f) the position for this acceleration is
x = A cos wt
x = A
x = 0.200 m
g) Mechanical energy is
Em = ½ k A²
Em = ½ 120 0.2²
Em = 2.4 J
h) the position is
x = 1/3 A
Let's calculate the time to reach this point
x = A cos wt
1/3 A = A cos 5.345t
t = 1 / w cos⁻¹(1/3)
The angles are in radians
t = 1.23 / 5,345
t = 0.2301 s
Speed is
v = -A w sin wt
v = -0.2 5.345 sin (5.345 0.2301)
v = -1.01 m / s
i) acceleration
a = -A w² sin wt
a = - 0.2 5.345² cos (5.345 0.2301)
a = -1.91 m / s²
Answer:
The time constant τ = L/R represent the time requiered for the curent to get value of 63 % of its maximun value
Explanation:
In a circuit RL ( serie circuit with a resistor R and the inductor L ) when a voltage is applied the inductor will have a reaction, such reaction consist in the creation of an electromotive force which will prevent the current to get its maximun value. The time constant which in the case of an inductor is
τ = L/R , represent the time requiered for the crrent to be 63 % of its final value
Answer: 5.79 s
Explanation:
Vs=0 m/s starting speed(from rest)
Vf=325 km/h= 325*1000/3600= 90.28 m/s
a=15.6m/s²
Using equation for acceleration we can find out time :
a=(Vf-Vs)/t
t=(Vf-Vs)/a
t=(90.28 m/s-0m/s)/15.6 m/s²
t=5.79 s
