Answer:
Explanation:
(a)
Applying the conservation of energy for cube,
i.e the initial kinetic energy of the body = its final potential energy
1/2mv² = mgh
h1 = v²/2g -------------------- (1)
and For cylinder,
the initial kinetic and rotational energy equals the final potential energy
1/2 mv² + 1/2 Iω² = mgh
here I = momentum of inertia of the cylinder
I = 1/2 m R²
∴ 1/2 mv² + 1/2 (1/2mR²)v²/R² = mgh
1/2 mv² + 1/4mv² = mgh
h2 = 3v²/4g -------------- (2)
From equations (1)&(2);
therefore the cylinder will go the greater distance up the incline.
(b)
h1-h2 = v²/2g - 3v²/4g
= 0.25 v²/g
the difference between the maximum distances the objects travel up the incline is 0.25*v²/g.
(c)
here we are taking into account of rotational energy.
Answer:
27 cm
Explanation:
ASSUMING the elevator is in a constant velocity state (could be zero)
mg = kx
x = mg/k = 15(9.8)/550 = 0.267272... m ≈ 27 cm
Answer:
a) 3.0 x 10¹⁰ J
b) 7.75 x 10³ m/s
Explanation:
a)
ΔV = potential difference between cloud and the ground = 1.0 x 10⁹ Volts
Q = Amount of charge transferred = 30 C
ΔU = Change in energy transferred
Change in energy transferred is given as
ΔU = Q ΔV
ΔU = (30) (1.0 x 10⁹)
ΔU = 3.0 x 10¹⁰ J
b)
v₀ = initial speed of the automobile = 0 m/s
v = final speed of the automobile = ?
m = mass of automobile = 1000 kg
Using conservation of energy
ΔU = (0.5) m (v² - v₀²)
3.0 x 10¹⁰ = (0.5) (1000) (v² - 0²)
v = 7.75 x 10³ m/s