Answer:
a) A = 0.603 m
, b) a = 165.8 m / s²
, c) F = 331.7 N
Explanation:
For this exercise we use the law of conservation of energy
Starting point before touching the spring
Em₀ = K = ½ m v²
End Point with fully compressed spring
= 
= ½ k x²
Emo =
½ m v² = ½ k x²
x = √(m / k) v
x = √ (2.00 / 550) 10.0
x = 0.603 m
This is the maximum compression corresponding to the range of motion
A = 0.603 m
b) Let's write Newton's second law at the point of maximum compression
F = m a
k x = ma
a = k / m x
a = 550 / 2.00 0.603
a = 165.8 m / s²
With direction to the right (positive)
c) The value of the elastic force, let's calculate
F = k x
F = 550 0.603
F = 331.65 N
Answer:
The magnification is 
Explanation:
From the question we are told that
The object distance is 
The focal length is 
From the lens equation we have that
=> 
substituting values
=> 
=> 
The magnification is mathematically represented as
substituting values
Answer:
t = 3.82 s
Ax = 147 N (←)
Ay = 294 N (+↑)
Explanation:
Given
m = 30.0 Kg
ωinitial = 125 rad/s
ωfinal = 0 rad/s
μC = 0.5
R = 0.3 m
t = ?
Ax = ?
Ay = ?
For the disk, we can apply
∑ τ = I*α
where I = m*R²/2
then
⇒ R*Ffriction = (m*R²/2)*α
⇒ R*(-μC*N) = R*(-μC*m*g) = (m*R²/2)*α
⇒ α = -2*μC*g / R
⇒ α = -2*(0.5)*(9.8) / 0.3 = -32.666 rad/s²
we can use the equation to get t:
α = Δω / t ⇒ t = Δω / α = (0 - 125) / (-32.666)
⇒ t = 3.82 s
The horizontal and vertical components of force which the member AB exerts on the pin at A during this time are
∑ Fx = 0 (+→)
Ax - Ffriction = 0
⇒ Ax = Ffriction = μC*m*g = (0.5)*(30)*(9.8) = 147 N
⇒ Ax = 147 N (←)
∑ Fy = 0 (+↑)
⇒ Ay - m*g = 0
⇒ Ay = m*g
⇒ Ay = 30*9.8 = 294 N
⇒ Ay = 294 N (+↑)
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)N= 21.29 rpm
Explanation:
Given that
Mass of the ball =m
Length of string = L
Lets take angular speed = ω
The centripetal force on the ball
F = m ω² L
To complete the circle ,at the top condition the force due to gravity should be equal to the centripetal force
Gravity force = mg
F= mg
m ω² L = m g
ω² L = g
When L= 2 m
Lets take g =10 m/s²
ω = 2.23 rad/s
To convert in rpm
N=Speed in rpm
N= 21.29 rpm
