Answer:
1.84 m
Explanation:
For the small lead ball to be balanced at the tip of the vertical circle just before it is released, the reaction force , N equal the weight of the lead ball W + the centripetal force, F. This normal reaction ,N also equals the tension T in the string.
So, T = mg + mrω² = ma where m = mass of small lead ball, g = acceleration due to gravity = 9.8 m/s², r = length of rope = 1.10 m and ω = angular speed of lead ball = 3 rev/s = 3 × 2π rad/s = 6π rad/s = 18.85 rad/s and a = acceleration of normal force. So,
a = g + rω²
= 9.8 m/s² + 1.10 m × (18.85 rad/s)²
= 9.8 m/s² + 390.85 m/s²
= 400.65 m/s²
Now, using v² = u² + 2a(h₂ - h₁) where u = initial velocity of ball = rω = 1.10 m × 18.85 rad/s = 20.74 m/s, v = final velocity of ball at maximum height = 0 m/s (since the ball is stationary at maximum height), a = acceleration of small lead ball = -400.65 m/s² (negative since it is in the downward direction of the tension), h₁ = initial position of lead ball above the ground = 1.3 m and h₂ = final position of lead ball above the ground = unknown.
v² = u² + 2a(h₂ - h₁)
So, v² - u² = 2a(h₂ - h₁)
h₂ - h₁ = (v² - u²)/2a
h₂ = h₁ + (v² - u²)/2a
substituting the values of the variables into the equation, we have
h₂ = 1.3 m + ((0 m/s)² - (20.74 m/s)²)/2(-400.65 m/s²)
h₂ = 1.3 m + [-430.15 (m/s)²]/-801.3 m/s²
h₂ = 1.3 m + 0.54 m
h₂ = 1.84 m
A finch rides on the back of a Galapagos tortoise, which walks at the stately pace of 0.060 m>s. After 1.5 minutes the finch tires of
Complete Question:
A finch rides on the back of a Galapagos tortoise, which walks
at the stately pace of 0.060 m/s. After 1.5 minutes the finch tires of
the tortoise’s slow pace, and takes flight in the same direction for
another 1.5 minutes at 11 m/s.
What was the average speed of the finch for this 3.0-minute interval?
Answer:
[tex]Speed = 5.53 m/s[/tex]
Explanation:
Distance is calculated as:
[tex]Distance = Speed * Time[/tex]
First, we calculate the distance for the first 1.5 minutes
For the first 1.5 minutes, we have:
[tex]Speed = 0.060m/s[/tex]
[tex]Time = 1.5\ mins[/tex]
[tex]D_2= 0.060m/s * 1.5\ mins[/tex]
Convert 1.5 mins to seconds
[tex]D_2= 0.060m/s * 1.5 * 60s[/tex]
[tex]D_2= 5.4m[/tex]
Next, we calculate the distance for the next 1.5 minutes
[tex]Speed = 11m/s[/tex]
[tex]Time = 1.5\ mins[/tex]
[tex]D_2= 11m/s * 1.5\ mins[/tex]
Convert 1.5 mins to seconds
[tex]D_2 = 11m/s * 1.5 * 60s[/tex]
[tex]D_2= 990m[/tex]
Total distance is:
[tex]Distance = 990m + 5.4m[/tex]
[tex]Distance = 995.4m[/tex]
The average speed for the 3.0 minute interval is:
[tex]Speed = \frac{Distance}{Time}[/tex]
[tex]Speed = \frac{995.4\ m}{3.0\ mins}[/tex]
Convert 3.0 minutes to seconds
[tex]Speed = \frac{995.4\ m}{3.0 * 60 secs}[/tex]
[tex]Speed = \frac{995.4\ m}{180 secs}[/tex]
[tex]Speed = 5.53 m/s[/tex]
Allen and Jason are chucking a speaker around. On one particular throw, Allen throws the speaker, which is playing a pure tone of frequency f, at a speed of 10 m/s directly towards Jason, but his aim is a bit off. As a result, Jason runs forward towards the speaker at a speed of 6 m/s before catching it. Then, the frequency that Jason hears while running can be written as (m/n)f Hz, where m and n are relatively prime positive integers. Compute m n.
Answer:
Explanation:
We shall apply Doppler's effect of sound .
speaker is the source , Jason is the observer . Source is moving at 10 m /s , observer is moving at 6 m/s .
apparent frequency = [tex]f_o\times\frac{V+v_o}{ V-v_s}[/tex]
V is velocity of sound , v₀ is velocity of observer and v_s is velocity of source and f_o is real frequency of source .
Here V = 340 m/s , v₀ is 6 m/s , v_s is 10 m/s . f_o = f
apparent frequency = [tex]f\times \frac{340+6}{340-10}[/tex]
= [tex]f\times \frac{346}{330}[/tex]
So m = 346 , n = 330 .
A 22.0 kg child is riding a playground merry-go- round that is rotating at 40.0 rev/min. What centripetal force must
Answer:
F = 482.51 N
Explanation:
Given that,
Mass of a child, m = 22 kg
Angular velocity of the merry-go-round, [tex]\omega=40\ rev/min[/tex]
Let the radius of the path, r = 1.25 m
We need to find the centripetal force acting on the child. The formula for the centripetal force is given by :
[tex]F=m\omega^2r\\\\=22\times (4.18879)^2\times 1.25\\\\=482.51\ N[/tex]
So, the required centripetal force is 482.51 N.
Scientists create models to better understand Earth. Which evidence has led scientists to conclude that there are different layers within Earth's interior?
A.analysis of seismic wave data
B.measurement of Earth's diameter
C.temperatures taken within each layer
D.rock samples taken from Earth's core
Answer:
it is A or D
Explanation:
Answer:
ANswer:A
Explanation:
The resistance of a wire depends on its length i and on its cross sectional area A the resistance is
Answer:
The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area
Explanation:
A hammer strikes a nail with a 10 N force for 0.01 seconds. Calculate the impulse of the hammer.
Answer:
0.1Ns
Explanation:
Impulse is the product of Force and time
Impulse = Force * Time
Given
Force = 10N
Time = 0.01s
Substitute into the formula
Impulse = 10 * 0.01
Impulse = 10 * 1/100
Impulse = 10/100
Impulse = 0.1Ns
hence the impulse of the hammer is 0.1Ns