Question:<em> </em><em>Find, separately, them mass of the balloon and the basket (incidentally, most of the balloon's mass is air)</em>
Answer:
The mass of the balloon is 2295 kg, and the mass of the basket is 301 kg.
Explanation:
Let us call the mass of the balloon 
and the mass of the basket 
, then according to newton's second law:
,
where 
is the upward acceleration, and 
is the net propelling force (counts the gravitational force).
Also, the tension 
in the rope is 79.8 N more than the basket's weight; therefore,
and this tension must equal
Combining equations (2) and (3) we get:
since , we have
Putting this into equation (1) and substituting the numerical values of 
and 
, we get:
Thus, the mass of the balloon and the basket is 2295 kg and 301 kg respectively.
Answer:
v = 8.09 m/s
Explanation:
For this exercise we use that the work done by the friction force plus the potential energy equals the change in the body's energy.
Let's calculate the energy
starting point. Higher
Em₀ = U = m gh
final point. To go down the slope
Em_f = K = ½ m v²
The work of the friction force is
W = fr L cos 180
to find the friction force let's use Newton's second law
Axis y
N - W_y = 0
N = W_y
X axis
Wₓ - fr = ma
let's use trigonometry
sin θ = y / L
sin θ = 11/110 = 0.1
θ = sin⁻¹ 0.1
θ = 5.74º
sin 5.74 = Wₓ / W
cos 5.74 = W_y / W
Wₓ = W sin 5.74
W_y = W cos 5.74
the formula for the friction force is
fr = μ N
fr = μ W cos θ
Work is friction force is
W_fr = - μ W L cos θ
Let's use the relationship of work with energy
W + ΔU = ΔK
-μ mg L cos 5.74 + (mgh - 0) = 0 - ½ m v²
v² = - 2 μ g L cos 5.74 +2 (gh)
v² = 2gh - 2 μ gL cos 5.74
let's calculate
v² = 2 9.8 11 - 2 0.07 9.8 110 cos 5.74
v² = 215.6 -150.16
v = √65.44
v = 8.09 m/s
Answer:
6 gallons
Explanation:
At 30 mph, the fuel mileage is 25 mpg.
After 5 hours, the distance traveled is:
30 mi/hr × 5 hr = 150 mi
The amount of gas used is:
150 mi × (1 gal / 25 mi) = 6 gal
I believe that it is the first one just a guess tho. So don't trust me, just in case
