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
Answer:
0 (Zero)
Explanation:
Definition of work done states that ,
Work done on an object is the force applied on that object in the direction of Displacement of the object .
means that ,
W = F.dS (Dot product of Force and displacement)
When the wall is acted upon by the force of 20 N , Wall does not move ,
Thus , displacement of the wall is zero.
So, W = 20×0 = 0.
Thus, Work done on the wall is zero.
Given: <span>ω(t) = 8.00 - 0.2*t^2
Differentiating both sides with respect to time we get:
angular acceleration = </span>α(t) = -0.2 * 2 *t
At t = 6.8 sec,
angular acceleration = α(t) = -0.2 * 2 *6.8 = -2.72 rad/s^2
Velocity of the bus = 75 miles/hr
Time taken by the bus to travel the distance between two cities = 2.5 hours
Let us assume the distance between the two cities = x
Then
Velocity = Distance/Time taken
Then Distance = Velocity * Time taken
= 75 * 2.5 miles
= 187.5 miles.
The distance between the two
cities is 187.5 miles.I hope this answer is what you were looking for. This
process is applicable for similar problems. In future you can always use this
method to determine the answer.
Answer:
a)
, b)
, c) 
Explanation:
a) The speed of the ball is determined by applying the Principle of Energy Conservation:

The speed of the ball when the string makes an angle of 12° with the vertical is:

![\frac{1}{2}\cdot m \cdot v^{2} = m\cdot g \cdot L \cdot [(1-\cos \theta_{1})-(1 -\cos \theta_{2})]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20m%20%5Ccdot%20v%5E%7B2%7D%20%3D%20m%5Ccdot%20g%20%5Ccdot%20L%20%5Ccdot%20%5B%281-%5Ccos%20%5Ctheta_%7B1%7D%29-%281%20-%5Ccos%20%5Ctheta_%7B2%7D%29%5D)



b) The maximum speed of the ball is:



c) The angle between the string and the vertical when the speed of the ball is one-third its maximum value is obtained by proving different values of
. The solution is approximately:
