The net force on an object is:
F = ma
The only force acting on the speck of dust as it is lays on the CD is centripetal force given by:
F = (mv²)/r
Equating the two
ma = (mv²)/r
We get:
a = v²/r
v is the linear velocity in this case; however, we can calculate only the angular velocity with the given data. Therefore, we must use:
v = ωr; where
ω = 2πf; f is the rotations per second
f = 9500 / 60
f = 950/6
ω = 2π(950/6)
ω = (950π)/3
v = (950π)/3 × 0.12
v = 38π
a = (38π)²/0.12
a = 1.2 × 10⁵ m/s²
To express this in terms of gravitational acceleration, we divide by the value of gravitational acceleration, 9.81
a = 1.2 × 10⁴ g
17.7m/s
Explanation:
Given parameters:
Height of branch = 16m
Unknown:
Velocity before falling = ?
Solution:
We are going to use the appropriate motion equation to solve this problem.
The bird is falling in line with the action of gravity.
Initial velocity is 0 for the bird.
Let the velocity during flight = V;
Then;
V² = U² + 2gH
since U = 0
V² = 2gH
V is the unknown velocity
H is the height of fall
g is the acceleration due to gravity
V = √2gH = √ 2x9.8 x 16 = 17.7m/s
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If you hear a clap of thunder in a time of 16.2s after seeing the associated lightning strike, you are: 5508 m far from the lightning strike
To solve this problem we must consider that the speed of light is greater than the speed of sound, therefore to calculate the distance we must use the speed of sound (340 m/s).
The formula and procedure we will use to solve this exercise is:
x = v * t
Where:
- x = distance
- t = time
- v = velocity
Information about the problem:
- v(sound) = 340 m/s
- t = 16.2 s
- x=?
Applying the distance formula we have that:
x = v * t
x= 340 m/s * 16.2 s
x = 5508 m
<h3>What is velocity?</h3>
It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
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The speed of sound in a solid would be 6000 metres per second
Answer:
C_{y} = 4.96 and θ' = 104,5º
Explanation:
To add several vectors we can decompose each one of them, perform the sum on each axis, to find the components of the resultant and then find the module and direction.
Let's start by decomposing the two vectors.
Vector A
sin θ =
/ A
cos θ = Aₓ / A
A_{y} = A sin θ
Ax = A cos θ
A_{y} = 4.9 sin 31 = 2.52
Ax = 4.9 cos 31 = 4.20
Vector B
B_{y} = B sin θ
Bx = B cos θ
B_{y} = 6 sin 156 = 2.44
Bx = 6 cos 156 = -5.48
The components of the resulting vector are
X axis
Cx = Ax + B x
Cx = 4.20 -5.48
Cx = -1.28
Axis y
C_{y} = Ay + By
C_{y} = 2.52 + 2.44
C_{y} = 4.96
Let's use the Pythagorean theorem to find modulo
C = √ (Cₙ²x2 + Cy2)
C = Ra (1.28 2 + 4.96 2)
C = 5.12
We use trigonemetry to find the angle
tan θ = C_{y} / Cₓ
θ’ = tan⁻¹ (4.96 / (1.28))
θ’ = 75.5
como el valor de Cy es positivo y Cx es negativo el angulo este en el segundo cuadrante, por lo cual el angulo medido respecto de eje x positivo es
θ’ = 180 – tes
θ‘= 180 – 75,5
θ' = 104,5º