Answers
Answer:
-384.22N
Explanation:
From Coulomb's law;
F= Kq1q2/r^2
Where;
K= constant of Coulomb's law = 9 ×10^9 Nm^2C-2
q1 and q2 = magnitudes of the both charges
r= distance of separation
F= 9 ×10^9 × −7.97×10^−6 × 6.91×10^−6/(0.0359)^2
F= -495.65 × 10^-3/ 1.29 × 10^-3
F= -384.22N
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For exercise, an athlete lifts a barbell that weighs 400 N from the ground to a height of 2.0 m in a time of 1.6 s. Assume the efficiency of the human body is 25%, and that he lifts the barbell at a constant speed. Show all work and include proper unit for your final answer.a) In applying the energy equation (ΔK + ΔUg + ΔUs + ΔEch + ΔEth = W) to the system consisting of the earth, the barbell, and the athlete,1. Which terms (if any) are positive?2. Which terms (if any) are negative?3. Which terms (if any) are zero? b) Determine the energy output by the athlete in SI unit.c) Determine his metabolic power in SI unit.d) Another day he performs the same task in 1.2 s.1. Is the metabolic energy that he expends more, less, or the same?2. Is his metabolic power more, less, or the same?
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Answers
A spinning disk's kinetic energy will change to one-tenth if its moment of inertia was five times larger but its angular speed was five times smaller.
Relation between Kinetic energy and Moment of Inertia:
- Rotational kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity.
Now, let's consider moment of inertia = I and angular speed = ω
It is asked that what would be change in Kinetic energy if
moment of inertia = (five times larger)
angular speed = ω/5 (five times smaller)
The kinetic energy of a spinning body is given as:
On substituting the values, we will get:
Kinetic energy will be one-tenth to the kinetic energy before its spinning characteristics were changed.
Learn more:
Answers
Answer:
The maximum spring compression = 3.21 m
Explanation:
The height of the circus performer above the platform connected to string material = 5.8 m
Let the maximum compression of the spring from the impact of the circus performer be x.
According to the law of conservation of energy, the difference in potential energy of the circus performer between the initial height and the level at which spring is compressed to is equal to the work done on the spring to compress it by x
Workdone on the spring by the circus performer = (1/2)kx²
where k = spring constant = 1200 N/m
Workdone on the spring by the circus performer = (1/2)(1200)x² = 600x²
The change in potential energy of the circus performer = mg (5.8 + x)
m = mass of the circus performer = 70 kg
g = acceleration due to gravity = 9.8 m/s²
The change in potential energy of the circus performer = (70)(9.8)(5.8 + x) = (3978.8 + 686x)
600x² = 3978.8 + 686x
600x² - 686x - 3978.8 = 0
Solving this quadratic equation
x = 3.21 m or - 2.07 m
Since the negative answer doesn't satisfy the laws of physics, our correct answer is 3.21 m
Hope this Helps!!!
Answers
Answer:
T1 = 499.9N, T2 = 865.8N, T3 = 1000N
Explanation:
To find the tensions we need to find the vertical and horizontal components of T1 and T2
T1x = T1 cos60⁰, T1y = T1 sin60⁰
Also, T2x = T2 cos30⁰, T2y = T2 sin30⁰
For the forces to be in equilibrium,
the sum of vertical forces must be zero and the sum of horizontal forces must also be zero
Sum of Fx = 0
That is, T1x - T2x=0
NB: T2x is being subtracted because T1x and T2x are in opposite directions
T1 cos60⁰ - T2 cos30⁰ = 0
0.866T1 - 0.5T2 = 0 ............ (1)
Sum of Fy = 0
T1y + T2y - 1000 = 0
T1 sin60⁰ + T2 sin30⁰ - 1000 = 0
NB: The weight of the bag of cement is also being subtracted because it's in an opposite direction.
0.5T1 - 0.866T2 - 1000 = 0 ........(2)
From (1)
make T1 the subject
T1 = 0.5T2/0.866
Substitute T1 into (2)
0.5 (0.5T2/0.866) - 0.866T2 = 1000
(0.25/0.866)T2 - 0.866T2 = 1000
0.289T2 - 0.866T2 = 1000
1.155T2 = 1000
T2 = 865.8N
Then T1 = 0.5 x 865.8 / 0.866
T1 = 499.9N
T3 = 1000N
NB: The weight of the bag is the Tension above the rope, which is T3
Answers
Answer and Explanation:
We know that resistance from the given equation of resistance it is clear that resistance depends on resistivity length and area of the material but we can not change the length because it is given that the length must be 2.5 cm long.
So we can do two two things to reduce the resistance
- increase the cross sectional area
- decrease the resistivity of the material
Answers
(a) See figure in attachment (please note that the image should be rotated by 90 degrees clockwise)
There are only two forces acting on the balloon, if we neglect air resistance:
- The weight of the balloon, labelled with W, whose magnitude is
where m is the mass of the balloon+the helium gas inside and g is the acceleration due to gravity, and whose direction is downward
- The Buoyant force, labelled with B, whose magnitude is
where is the air density, V is the volume of the balloon and g the acceleration due to gravity, and where the direction is upward
(b) 4159 N
The buoyant force is given by
where is the air density, V is the volume of the balloon and g the acceleration due to gravity.
In this case we have
is the air density
is the volume of the balloon
g = 9.8 m/s^2 is the acceleration due to gravity
So the buoyant force is
(c) 1524 N
The mass of the helium gas inside the balloon is
where is the helium density; so we the total mass of the balloon+helium gas inside is
So now we can find the weight of the balloon:
And so, the net force on the balloon is
(d) The balloon will rise
Explanation: we said that there are only two forces acting on the balloon: the buoyant force, upward, and the weight, downward. Since the magnitude of the buoyant force is larger than the magnitude of the weigth, this means that the net force on the balloon points upward, so according to Newton's second law, the balloon will have an acceleration pointing upward, so it will rise.
(e) 155 kg
The maximum additional mass that the balloon can support in equilibrium can be found by requiring that the buoyant force is equal to the new weight of the balloon:
where m' is the additional mass. Re-arranging the equation for m', we find
(f) The balloon and its load will accelerate upward.
If the mass of the load is less than the value calculated in the previous part (155 kg), the balloon will accelerate upward, because the buoyant force will still be larger than the weight of the balloon, so the net force will still be pointing upward.
(g) The decrease in air density as the altitude increases
As the balloon rises and goes higher, the density of the air in the atmosphere decreases. As a result, the buoyant force that pushes the balloon upward will decrease, according to the formula
So, at a certain altitude h, the buoyant force will be no longer greater than the weight of the balloon, therefore the net force will become zero and the balloon will no longer rise.
Final answer:
The physics involved in the functioning of helium balloons is based on buoyancy and Archimedes' Principle. The forces at play include the force due to gravity, the buoyant force and the net force, which determines the motion of the balloon. The balloon's height limit is determined by the decrease in air density with altitude.
Explanation:
The several parts of this question are related to the principles of buoyancy and Archimedes' Principle. First, regarding the force diagram for the balloon (part a), it would show two primary forces. The force due to gravity (Fg) acting downwards and the buoyant force (Fb) acting upwards, which is a result of the displacement of air by the balloon. The net force mentioned in part (c) is calculated as the difference between these two forces.
Calculating the buoyant force (part b) involves multiplying the volume of the balloon by the density of the air and the acceleration due to gravity (Fb = V * ρ_air * g). For the net force on the balloon (part c), this is calculated by subtracting the weight of the balloon from the buoyant force (F_net = Fb - Fg). If the net force is positive, the balloon will rise, if it's negative, the balloon will fall, and if it is zero, the balloon will remain stationary.
The maximum additional mass the balloon can support in equilibrium (part d) is calculated using the net force divided by gravity. If the mass of the load is less than this value (part e), the balloon and its load will accelerate upward.
Lastly, the limit to the height to which the balloon can rise (part f) is determined by the decreasing density of the air as the balloon ascends. The buoyant force reduces as the balloon rises because the air density is lower at higher altitudes.
Learn more about Buoyancy here:
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Answers
Answer:
mnbhngbfcvdxc
Explanation: