Answer:
a) K = 0.63 J, b) h = 0.153 m
Explanation:
a) In this exercise we have a physical pendulum since the rod is a material object, the angular velocity is
w² = 
where d is the distance from the pivot point to the center of mass and I is the moment of inertia.
The rod is a homogeneous body so its center of mass is at the geometric center of the rod.
d = L / 2
the moment of inertia of the rod is the moment of a rod supported at one end
I = ⅓ m L²
we substitute
w = 
w = 
w = 
w = 4.427 rad / s
an oscillatory system is described by the expression
θ = θ₀ cos (wt + Φ)
the angular velocity is
w = dθ /dt
w = - θ₀ w sin (wt + Ф)
In this exercise, the kinetic energy is requested in the lowest position, in this position the energy is maximum. For this expression to be maximum, the sine function must be equal to ±1
In the exercise it is indicated that at the lowest point the angular velocity is
w = 4.0 rad / s
the kinetic energy is
K = ½ I w²
K = ½ (⅓ m L²) w²
K = 1/6 m L² w²
K = 1/6 0.42 0.75² 4.0²
K = 0.63 J
b) for this part let's use conservation of energy
starting point. Lowest point
Em₀ = K = ½ I w²
final point. Highest point
Em_f = U = m g h
energy is conserved
Em₀ = Em_f
½ I w² = m g h
½ (⅓ m L²) w² = m g h
h = 1/6 L² w² / g
h = 1/6 0.75² 4.0² / 9.8
h = 0.153 m
Answer:
126.56 m
Explanation:
Applying,
-F = ma............. Equation 1
Where F = frictional force, m = mass of the car, a = acceleration.
Note: Frictional force is negative because it act in opposite direction to motion
But,
F = mgμ.......... Equation 2
Where g = acceleration due to gravity, μ = coefficient of friction
Substitute equation 2 in equation 1
-mgμ = ma
a = -gμ.............. Equation 3
From the question,
Given: μ = 0.735
Constant: 9.8 m/s²
Substitute these values in equation 3
a = -9.8×0.735
a = -7.203 m/s²
Finally,
Applying
v² = u²+2as.............. Equation 4
Where v = final velocity, u = initial velocity, s = distance
From the question,
Given: u = 42.7 m/s, v = 0 m/s (to a stop), a = -7.203 m/s²
Substitute these values into equation 4
0² = 42.7²+2(-7.203)s
-1823.29 = -14.406s
s = -1823.29/-14.406
s = 126.56 m
The answer i think would be D
Answer:
h = 90.10 m
Explanation:
Given that,
A man is standing near the edge of a cliff 85 meters high, h₀ = 85 m
The initial speed of the stone, u = 10 m/s
The path followed by the projectile is given by :
....(1)
For maximum height,
Put dh/dt = 0
So,
Put the value of t in equation (1).
So, the maximum height of the stone is equal to 90.10 m.
<span>The question is asking us to fill in the gap in: (gap) is a force of attraction that occurs between objects due to their mass.The correct answer is b. gravity. People don't know that gravity works both ways: both objects atract each. The reason why we're more attracted to Earth than Earth is pulled to us is that Earth has a much higher mass - the bigger the mass, the stronger the atraction</span>
