a bowling ball has a mass of 6 kilograms. a tennis ball has a mass of 0.06 kilogram. how much inertia does the bowling ball have
compared to the tennis ball?
1 answer:
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THE GREEN HOSE:
Define the (x,y) coordinate at a height of 4 feet up from the ground to match where Majra is holding the green hose.
This means that the equation for the green hose is of the form
y = a(x - h)² + 4 (1)
Because water from the green hose lands on the ground 10 feet from where Majra is standing, therefore
y(10) = -4 (2)
Because the curve passes through (0,0), therefore
ah² + 4 = 0
ah² = - 4 (3)
To satisfy (2), obtain
a(10 - h)² + 4 = -4
a(10 - h)² = - 8 (4)
Divide (3) by (4).
h²/(10-h)² = 1/2
2h² = (10 - h)² = 100 - 20h + h²
h² + 20h - 100 = 0
Solve with the quadratic formula.
x = 0.5[-20 +/- √(8400)] = 4.142, - 24.142
Reject the negative solution.
The vertex is at (4.142, 4).
From (3), obtain
a = -4/4.142² = -0.2332
The equation for the green hose is
y = 0.2332(x - 4.142)² + 4
THE RED HOSE
The red hose has a vertex at (3,7), according to the equation y = -(x-3)² + 7.
A graph of y(x) for both hoses is shown in the attached figure.
Answers:
a. The red hose will throw the water higher.
b. The equation for the green hose is
y = -0.2332(x - 4.124)² + 4,
with the origin at a height of 4 feet above ground level.
c. The domain for the green hose that makes sense is 0 ≤ x ≤ 10 feet.
The corresponding range is -4 ≤ y ≤ 4 feet.
Define the (x,y) coordinate at a height of 4 feet up from the ground to match where Majra is holding the green hose.
This means that the equation for the green hose is of the form
y = a(x - h)² + 4 (1)
Because water from the green hose lands on the ground 10 feet from where Majra is standing, therefore
y(10) = -4 (2)
Because the curve passes through (0,0), therefore
ah² + 4 = 0
ah² = - 4 (3)
To satisfy (2), obtain
a(10 - h)² + 4 = -4
a(10 - h)² = - 8 (4)
Divide (3) by (4).
h²/(10-h)² = 1/2
2h² = (10 - h)² = 100 - 20h + h²
h² + 20h - 100 = 0
Solve with the quadratic formula.
x = 0.5[-20 +/- √(8400)] = 4.142, - 24.142
Reject the negative solution.
The vertex is at (4.142, 4).
From (3), obtain
a = -4/4.142² = -0.2332
The equation for the green hose is
y = 0.2332(x - 4.142)² + 4
THE RED HOSE
The red hose has a vertex at (3,7), according to the equation y = -(x-3)² + 7.
A graph of y(x) for both hoses is shown in the attached figure.
Answers:
a. The red hose will throw the water higher.
b. The equation for the green hose is
y = -0.2332(x - 4.124)² + 4,
with the origin at a height of 4 feet above ground level.
c. The domain for the green hose that makes sense is 0 ≤ x ≤ 10 feet.
The corresponding range is -4 ≤ y ≤ 4 feet.
The skateboarder will have the greatest potential energy at point <em>G.</em>
Potential energy is the energy possessed by a body by virtue of its position. The gravitational potential energy of a body is given by the expression,
Here, <em>m</em> is the mass of the body, <em>g</em> the acceleration due to gravity and <em>h</em> is the height of the body from the ground.Thus as <em>h</em> increases, the potential energy increases.
From the figure, it can be seen that the highest point in the skateboarder's trajectory is <em>G.</em> hence, he would have the highest potential energy at the point <em>G.</em>
Answer:
g' = g/4
Explanation:
- The value of the free-fall acceleration at the surface of the earth, can be obtained applying Newton's 2nd law, assuming that the only force acting on an object at the surface of the earth, is the one produced by the mass of the Earth, i.e. gravity.
- This force can be expressed according the Newton's Universal Law of Gravitation , as follows:
- From Newton's 2nd Law, we have:
- Since the left sides in (1) and (2) are equal each other, both right sides must be equal each other also.
- Simplifying the mass m, we can write the acceleration a in (2) as the acceleration due to gravity, g, as follows:
- Since G is an universal constant, and the mass mE remains constant, if we double the radius of the Earth, the new value for the acceleration due to gravity (let's call it g'), is as follows:
Answer: a) Moment = 200N.m
b) F = 500N
Explanation: <u>Moment</u> or <u>Torque</u> is the tendency of a body to rotate because of an aplplied force. It can be calculated as
F is force applied
r is distance from the force to the point of rotation
θ is the angle formed between force and distance
a) Since F and r are perpendicular, θ=90°, sin90° = 1, so
200
<u>Torque</u><u> caused by weight of the barrier at the pivot is </u><u>200N.m</u>
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b) Counterweight has the same torque as pivot: 200
So, to find Force necessary to balance the weight:
F = 500
<u>It is necessary </u><u>a force of 500N</u><u> from the counterweight to balance the weight.</u>
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