Setting reference frame so that the x axis is along the incline and y is perpendicular to the incline
<span>X: mgsin65 - F = mAx </span>
<span>Y: N - mgcos65 = 0 (N is the normal force on the incline) N = mgcos65 (which we knew) </span>
<span>Moment about center of mass: </span>
<span>Fr = Iα </span>
<span>Now Ax = rα </span>
<span>and F = umgcos65 </span>
<span>mgsin65 - umgcos65 = mrα -------------> gsin65 - ugcos65 = rα (this is the X equation m's cancel) </span>
<span>umgcos65(r) = 0.4mr^2(α) -----------> ugcos65(r) = 0.4r(rα) (This is the moment equation m's cancel) </span>
<span>ugcos65(r) = 0.4r(gsin65 - ugcos65) ( moment equation subbing in X equation for rα) </span>
<span>ugcos65 = 0.4(gsin65 - ugcos65) </span>
<span>1.4ugcos65 = 0.4gsin65 </span>
<span>1.4ucos65 = 0.4sin65 </span>
<span>u = 0.4sin65/1.4cos65 </span>
<span>u = 0.613 </span>
Answer:
h₍₁₎ = 495,1 meters
h₍₂₎ = 480,4 m
h₍₃₎ = 455,9 m
...
..
Explanation:
The exercise is "free fall". t = 
Solving with this formula you find the time it takes for the stone to reach the ground (T) = 102,04 s
The heights (h) according to his time (t) are found according to the formula:
h(t) = 500 - 1/2 * g * t²
Remplacing "t" with the desired time.
Answer:
N = 177843 sheets
Explanation:
We are given;
Mass;m = 0.0035 kg
Pressure; p = 101325 pa = 101325 N/m²
L = 0.279m
W = 0.216m
The weight of N sheets is N(mg)
Where;
m is the mass of one sheet
N is number of sheets
g is the acceleration due to gravity.
The pressure equals weight divided by the area on which the weight presses:
Thus,
p= F/A = Nmg/(L•W)
Therefore, making N the subject;
N = pLW/(mg)
N = 101325 x 0.279 x 0.216/ (0.0035 x 9.81)
N = 177843
Answer:
342 m/s
Explanation:
The velocity of sound in air is approximated as:
v ≈ 331.4 + 0.6 T
where v is the velocity in m/s and T is the temperature in Celsius.
At T = 18:
v ≈ 331.4 + 0.6 (18)
v ≈ 342.2
The velocity is approximately 342 m/s.
