Answer:
a) A:170572.5 J
C: 55794.9J
b) 170572.5 J
c) 41.4413265306m
d) 2.7455874717m/s
Explanation:
a) Kinetic energy = 0.5*m*v²
KE at A = 0.5*420*28.5² = 170572.5 J
KE at C = 0.5*420*16.3² = 55794.9 J
b) Mechanical energy is the total kinetic energy plus potential energy at a point on the system. There is no potential energy at A.
ANSWER: 170572.5 J
c) v²=u²+2as
28.5²=2(9.8)s
812.25/19.6=s
s=41.4413265306m
d) h=height from part c, r=radius of loop
v²=u²+2as
v²=gr or a=v²/r
Ei=Ef
mgh=0.5mv²+mg(2r)
gh=0.5v²+2gr
h=0.5r+2r
h=5/2r
r=2/5h=(2/5)(41.4413265306)=16.5765306122
F=ma
mg=m(v²/r)
g=v²/r
v²=(9.8)(16.5765306122)
v=√162.45
=12.7455874717m/s
Define brown horse:
a₁ = 2.2 m/s², acceleration
v₁ = 18 m/s, top speed
Define the black horse:
a₂ = 1.7 m/s², accelerastopn
v₂ = 20 m/s, maximum speed
To travel 2000m, each horse accelerates to maximum speed, and cruises to the finish line.
For the brown horse:
The time to attain maximum speed is
t₁₁ = v₁/a₁ = 18/2.2 = 8.182 s
The distance travelled during the acceleration is
s = (1/2)*a*t² = 0.5*2.2*8.182² = 73.636 m
The time to travel the remaining distance is
t₁₂ = (2000 - 73.636)/18 = 107.02 s
The total time of travel is
t₁ = t₁₁ + t₁₂ = 8.182 + 107.02 = 115.2 s (approx)
For the black horse:
Time to attain maximum speed is
t₂₁ = 20/1.7 = 11.765 s
Distance traveled while accelerating is
0.5*(1.7 m/s²)*(11.765 s)² = 117.647 m
Time to travel the remaining distance is
t₂₂ = (2000 - 117.647)/20 = 94.118 s
The total time of travel is
t₂ = t₂₁ + t₂₂ = 11.765 + 94.118 = 105.9 s (approx)
Conclusion:
The black horse wins the race in about 106 s, while the brown horse takes about 115 s
Answer: The black horse wins.
Answer:
8.475 x 10^7 Pa
Explanation:
h = 8648 m, g = 9.8 m/s^2, density of water, d = 1000 kg/m^3
Pressure at a depth is defined as the product of depth of water , acceleration due to gravity and density of water.
P = h x d x g
P = 8648 x 1000 x 9.8 = 8.475 x 10^7 Pa