Answer:
80 meters high
Explanation:
The velocity of the balloon would be g*t (I won't calculate, but will us this later)
We know that the kinetic energy at the bottom equals the potential at the top.
KE = PE
1/2 * m * v^2 = m * g * h
1/2 * m * (g * t)^2 = m * g * h (substitution)
1/2 * m * g^2 * t^2 = m * g * h
1/2 * g * t^2 = h (simplification by dividing the commons between both sides)
h = 1/2 * 9.81 * 4^2
h = 78.48 m (roughly 80 m)
(A) The speed of the pendulum when it reaches the bottom is 3.83 m/s.
(B) The speed of the pendulum when it reaches the bottom after losing 18% of its energy is 3.47 m/s.
(C) The height reached by the pendulum after losing another 7% of its energy is 0.57 m.
(D) When the pendulum stops swinging, it has used all its energy to overcome frictional force of air.
<h3>
Speed of the pendulum when it reaches the bottom</h3>
Apply the principle of conservation of energy;
K.E = P.E
¹/₂mv² = mgh
v² = 2gh
v = √2gh
v = √(2 x 9.8 x 0.75)
v = 3.83 m/s
<h3>Speed pendulum after losing 18% of the its initial energy</h3>
K.E = (100 - 18)P.E
¹/₂mv² = 0.82mgh
V = √(0.82 x 2gh)
v = √(0.82 x 2 x 9.8 x 0.75)
v = 3.47 m/s
<h3>Height reached when its looses another 7%</h3>
K.E = 0.5(1)(3.47)² = 6.02 J
When it losses 7% = 6.02 - (0.07 x 6.02) = 5.598 J
Height reached:
mgh = 5.598
h = 5.598/mg
h = 5.598/(1 x 9.8)
h = 0.57 m
<h3>Final energy of the pendulum</h3>
When the pendulum stops swinging, it has used all its energy to overcome frictional force of air.
Thus, the speed of the pendulum when it reaches the bottom is 3.83 m/s.
The speed of the pendulum when it reaches the bottom after losing 18% of its energy is 3.47 m/s.
The height reached by the pendulum after losing another 7% of its energy is 0.57 m.
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Answer:
1/Rt = 1/R1 + 1/R2 + 1/R3 +...
Explanation:
Density = Mass / Volume
Mass = Density * Volume
Mass = 30 g/cm³ * 10 cm³ = 300 g
Mass = 300 g
The mass of the car should be A) 1212 kg
Explanation:
We can solve the problem by using Newton's second law of motion, which states that

where:
F is the force produced by the engine
m is the mass of the car
a is its acceleration
In the first situation we have
m = 1515 kg
is the acceleration
Solving for F, we find the force produced by the engine:

Now we want the car to reach an acceleration of

Using the same engine, therefore the force produced is still
F = 18,180 N
Re-arranging the equation for m', we find what should be the new mass of the car:

Learn more about Newton's second law:
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