Let's break the problem into two parts:
1) In the first part, the wheel starts with an angular speed
and it rotates with an angular acceleration of
for t=1.80 s. So we can find the total angle covered by the wheel in this part of the motion:
2) Now, the circuit breaker trips, so the wheel starts to decelerate with a certain angular acceleration
(which is negative). During this part of the motion, the wheel covered an angle of
.
3) So, we just need to add the angles the wheel covered in the two parts of the motion:
Answer:
Therefore maximum stretch is y2 = 32.36 m
Explanation:
In this problem let's use the initial data to find the string constant, let's apply Newton's second law when in equilibrium
- W = 0
k Δx = mg
k = mg / Δx
k = 80 9.8 / (30-20)
k = 78.4 N / m
now let's use conservation of energy to find the velocity of the body just as the string starts to stretch y = 20 m
starting point. When will you jump
Em₀ = U = mg y
final point. Just when the rope starts to stretch
= K = ½ m v²
Em₀ = Em_{f}
mg y = ½ m v²
v = √ 2g y
v = √ (2 9.8 20)
v = 19.8 m / s
now all kinetic energy is transformed into elastic energy
starting point
Em₀ = K = ½ m v²
final point
Em_{f} = + U = ½ k y² + m g y
Emo = Em_{f}
½ m v² = ½ k y² + mgy
k y² + 2 m g y - m v² = 0
we substitute the values and solve the quadratic equation
78.4 y² + 2 80 9.8 y - 80 19.8² = 0
78.4 y² + 1568 y - 31363.2 = 0
y² + 20 y - 400 = 0
y = [- 20 ±√ (20 2 +4 400)] / 2
y = [-20 ± 44.72] / 2
the solutions are
y₁ = 12.36 m
y₂ = 32.36 m
These solutions correspond to the maximum stretch and its rebound.
Therefore maximum stretch is y2 = 32.36 m
G= 9.8m/s^2 =
Well, think about the fall times and calculate the equation and then you will be able to solve G= 9.8m/s^2
I think G= gravity (I haven't learned this yet :P)
So gravity = 9.8m ( m = variable)
/s^2 (/= division) (s^2 =1 S(2)
(2 as power)
So if you set this up you will come up with[Gravity 9.8 multiplied by m divided by 1 multiplied by S(2)
I have never done something like this before so hope I got it right :)
The answer is C.
I just took the test!
Hope this helps. :)