Answer: 96.138 J
Explanation:
Use equation for potential gravitational energy : Ep=mGh
Ep1=mGh1
Ep2=mGh2
-------------
Ep1= 3.5*9.81*1.2
Ep1=41.202 J
Ep2=3.5*9.81*4
Ep2=137.34 J
Ep=Ep2-Ep1
Ep=137.34-41.202
Ep= 96.138 J
To solve this, we
use the formula:
y = v0 t + 0.5 a t^2
where y is distance, v0 is initial velocity, t is time
and a is acceleration
Since we know that total time is 8.5 seconds, hence going
up must be 4.25 s and going down is 4.25 s.
a = 0.379 g = 0.379 (9.8 m/s^2) = 3.7142 m/s^2
going up:
y = v0 (4.25) - 0.5 (3.7142) (4.25)^2
y = 4.25 v0 – 33.5439 -->
eqtn 1
going down:
y = 0 (4.25) + 0.5 (3.7142) (4.25)^2
y = 33.5439
y = 33.5439 m
Calculating for v0 from equation 1:
33.5439 = 4.25 v0 – 33.5439
4.25 v0 = 67.0877
v0 = 15.78535 m/s
answers:
a. y = 33.5439 m
b. v0 = 15.78535 m/s
c.
Answer:
table and graph are attached
Explanation:
a) The velocity of the ball will be ...
v(t) = v0 -at
v(t) = 19.6 -9.8t
The position of the ball will be the integral of this:
h(t) = ∫v(t)·dt = 19.6t -(1/2)(9.8t^2)
The attached table calculates the vertical position in meters for the required times.
__
b) Graphs of displacement (h(t)) and velocity (h'(t)) are shown in the attachment.
Answer:
189 m/s
Explanation:
The pilot will experience weightlessness when the centrifugal force, F equals his weight, W.
So, F = W
mv²/r = mg
v² = gr
v = √gr where v = velocity, g = acceleration due to gravity = 9.8 m/s² and r = radius of loop = 3.63 × 10³ m
So, v = √gr
v = √(9.8 m/s² × 3.63 × 10³ m)
v = √(35.574 × 10³ m²/s²)
v = √(3.5574 × 10⁴ m²/s²)
v = 1.89 × 10² m/s
v = 189 m/s
