Answer:
The tangential speed of the ball is 11.213 m/s
Explanation:
The radius is equal:
(ball rotates in a circle)
If the system is in equilibrium, the tension is:
Replacing:
Replacing:
Mass of the displaced material. In water it would be the mass of the water that the volume of the ball displaces.
Answer:
a) The magnitude of the force is 968 N
b) For a constant speed of 30 m/s, the magnitude of the force is 1,037 N
Explanation:
<em>NOTE: The question b) will be changed in other to give a meaningful answer, because it is the same speed as the original (the gallons would be 1.9, as in the original).</em>
Information given:
d = 106 km = 106,000 m
v1 = 28 m/s
G = 1.9 gal
η = 0.3
Eff = 1.2 x 10^8 J/gal
a) We can express the energy used as the work done. This work has the following expression:
Then, we can derive the magnitude of the force as:
b) We will calculate the force for a speed of 30 m/s.
If the force is proportional to the speed, we have:
Answer:
Vf = 15 m/s
Explanation:
First we consider the upward motion of ball to find the height reached by the ball. Using 3rd equation of motion:
2gh = Vf² - Vi²
where,
g = acceleration due to gravity = -9.8 m/s² (negative sign for upward motion)
h = height =?
Vf = Final Velocity = 0 m/s (Since, ball momentarily stops at highest point)
Vi = Initial Velocity = 15 m/s
Therefore,
2(-9.8 m/s²)h = (0 m/s)² - (15 m/s)²
h = (-225 m²/s²)/(-19.6 m/s²)
h = 11.47 m
Now, we consider downward motion:
2gh = Vf² - Vi²
where,
g = acceleration due to gravity = 9.8 m/s²
h = height = 11.47 m
Vf = Final Velocity = ?
Vi = Initial Velocity = 0 m/s
Therefore,
2(9.8 m/s²)(11.47 m) = Vf² - (0 m/s)²
Vf = √(224.812 m²/s²)
<u>Vf = 15 m/s</u>
Answer:
1) John's ball lands last.
2) All three have the same total energy
Explanation:
John's ball will land last because his ball was projected at the largest angle. This means that the ball will spend more time in the air when compared to the other balls.
The total energy in a projected particle is the sum of its kinetic energy (0.5mv^2) and its potential energy due to its height (mgh). The total kinetic energy can be as a result of both, or at times fully transformed to either of the energy. For example, at the maximum height, the kinetic energy of John's ball is zero and is fully transformed into potential energy due to that height, whereas George's ball will mostly posses kinetic energy and a little potential energy. The three ball are assumed to have the same properties and are projected with the same initial velocity. This means that they all have the same kinetic energy at the instance of projection which can then be transformed into potential energy, or maintained as a combination of both throughout the flight or simply transformed into potential energy, but the total energy is always conserved.
