Answer:
a) w = 2.57 rad / s
, b) α = 3.3 rad / s²
Explanation:
a) Let's use the conservation of mechanical energy, we will write it in two points the highest and when touching the ground
Initial. Higher
Em₀ = U = m g h
Final. Touching the ground
= K = ½ I w²
How energy is conserved
Em₀ =
mg h = ½ I w2
The moment of specific object inertia
I = m L²
We replace
m g h = ½ (mL²) w²
w² = 2g h / L²
The height of the object is the length of the bar
h = L
w = √ 2g / L
w = √ (2 9.8 / 2.97)
w = 2.57 rad / s
b) the angular acceleration can be found from Newton's second rotational law
τ = I α
W L = I α
mg L = (m L²) α
α = g / L
α = 9.8 / 2.97
α = 3.3 rad / s²
To solve the problem you must first know that by keeping the linear moment P1 = P2. You must find P1 from the system and equal it to P2 of the system, from that equation you clear the final velocity 1. Which will result in V1f = 60.16 cm / s to the north.I attach the solution.
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Momentum, p = m.v
m of the girl = 60.0 kg
m of the boat = 180 kg
v of the girl = 4.0 m/s
A) Momentum of the girl as she is diving:
p = m.v = 60.0 kg * 4.0 m/s = 24.0 N/s
B) momentum of the raft = - momentum of the girl = -24.0 N/s
C) speed of the raft
p = m.v ; v = p/m = 24.0N/s / 180 kg = -0.13 m/s [i.e. in the opposite direction of the girl's velocity]
<span>An object roating at one revokution per second has an angular velocity of 360 degrees per second or 2pi radians per second. This is found by taking the number of revolutions over a period of time and than dividing by the chosen period of time to get the velocity. There are 360 degrees or 2pi radians in one revolution.</span>
