Answer:
1.8 s
Explanation:
Potential energy = kinetic energy + rotational energy
mgh = ½ mv² + ½ Iω²
For a thin spherical shell, I = ⅔ mr².
mgh = ½ mv² + ½ (⅔ mr²) ω²
mgh = ½ mv² + ⅓ mr²ω²
For rolling without slipping, v = ωr.
mgh = ½ mv² + ⅓ mv²
mgh = ⅚ mv²
gh = ⅚ v²
v = √(1.2gh)
v = √(1.2 × 9.81 m/s² × 4.8 m sin 39.4°)
v = 5.47 m/s
The acceleration down the incline is constant, so given:
Δx = 4.8 m
v₀ = 0 m/s
v = 5.47 m/s
Find: t
Δx = ½ (v + v₀) t
t = 2Δx / (v + v₀)
t = 2 (4.8 m) / (5.47 m/s + 0 m/s)
t = 1.76 s
Rounding to two significant figures, it takes 1.8 seconds.
Answer:
1 through 92 occur naturally on Earth
S.G. or specific gravity is the ratio of the density of an object to a fluid. It also is the fraction of the object's volume that would be submerged if the object were placed in the fluid. (note: if S.G.>1, the object will sink)
S.G. = density(wood) / density(water)
2/3 = density(wood) / 1000
density(wood) = 2000/3 kg/m^3 = ~666.67 kg/m^3
S.G. = density(wood) / density(oil)
9/10 = 2000/3 / density(oil)
density(oil) = 2000/3 / 9/10 = 20000/27 kg/m^3 = ~740.74 kg/m^3
