A 350-g baseball is shot out of a small cannon with a velocity of 9.0 m/s. The baseball flies horizontally at a constant height
1 answer:
Answer:
Explanation:
The angular momentum of an object is given by:
where
m is the mass of the object
v is its velocity
r is the distance of the object from axis of rotation
Here we have:
m = 350 g = 0.35 kg is the mass of the ball
v = 9.0 m/s is the velocity
r = 3.0 m is the distance of the object from axis of rotation (if we take the ground as the centre of rotation)
Therefore, the angular momentum is:
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Answer:
The tension in the string is 16.24 N
Explanation:
Given;
mass of the sphere, m = 1.55 kg
initial velocity of the sphere, u = 2.81 m/s
final velocity of the sphere, v = 4.60 m/s
duration of change in the velocity, Δt = 2.64 s
The tension of the string is calculated as follows;
T = 1.55(0.678 + 9.8)
T = 1.55(10.478)
T = 16.24 N
Therefore, the tension in the string is 16.24 N
To solve this problem we will apply the concepts related to centripetal acceleration, which will be the same - by balance - to the force of gravity on the body. To find this acceleration we must first find the orbital velocity through the Doppler formulas for the given periodic signals. In this way:
Here,
Orbital Velocity
Maximal Wavelength
Average Wavelength
c = Speed of light
Replacing with our values we have that,
<em>Note that the average signal is 3.000000m</em>
Now using the definition about centripetal acceleration we have,
Here,
v = Orbit Velocity
r = Radius of Orbit
Replacing with our values,
Applying Newton's equation for acceleration due to gravity,
Here,
G = Universal gravitational constant
M = Mass of the planet
r = Orbit
The acceleration due to gravity is the same as the previous centripetal acceleration by equilibrium, then rearranging to find the mass we have,
Therefore the mass of the planet is