Answer:
a. v₁ = 16.2 m/s
b. μ = 0.251
Explanation:
Given:
θ = 15 ° , r = 100 m , v₂ = 15.0 km / h
a.
To determine v₁ to take a 100 m radius curve banked at 15 °
tan θ = v₁² / r * g
v₁ = √ r * g * tan θ
v₁ = √ 100 m * 9.8 m/s² * tan 15° = 16.2 m/s
b.
To determine μ friction needed for a frightened
v₂ = 15.0 km / h * 1000 m / 1 km * 1h / 60 minute * 1 minute / 60 seg
v₂ = 4.2 m/s
fk = μ * m * g
a₁ = v₁² / r = 16.2 ² / 100 m = 2.63 m/s²
a₂ = v₂² / r = 4.2 ² / 100 m = 0.18 m/s²
F₁ = m * a₁ , F₂ = m * a₂
fk = F₁ - F₂ ⇒ μ * m * g = m * ( a₁ - a₂)
μ * g = a₁ - a₂ ⇒ μ = a₁ - a₂ / g
μ = [ 2.63 m/s² - 0.18 m/s² ] / (9.8 m/s²)
μ = 0.251
The acceleration of the body is 2 m/s^2 while the deceleration is - 1.2 m/s^2.
<h3>
What is the acceleration?</h3>
Let us recall that the acceleration is the change in the speed of a body with time. We have been told that the body accelerates for 3s and then decelerates to 2s. This implies that the total time that the object spent in motion is 5 s.
Thus;
v = u + at
v = final velocity
u = initial velocity
a = acceleration
t = time taken
v - u/t = a
a = 6 - 0/3
= 2 m/s^2
Again;
v - u/t = a
a = 0 - 6/5
a = - 1.2m/s^2
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<h3 />
The new gravitational attraction will be 1/4 as much
Explanation:
The magnitude of the gravitational force between two objects is given by
where
is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between them
In this problem, the original force between the two objects is F, when they are separated by a distance r.
Later, the distance between the two objects is doubled, so the new distance is

Therefore, the new force will be

Therefore, the new force will be one-fourth as much.
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Answer:1.71 m/s
Explanation:
Given
mass of Susan 
Inclination 
Tension 
coefficient of Friction 
Resolving Forces Along x axis

where

since there is no movement in Y direction therefore

and 
Thus 


Work done by applied Force is equal to change to kinetic Energy



