Answer:
41°
Explanation:
Kinetic energy at bottom = potential energy at top
½ mv² = mgh
½ v² = gh
h = v²/(2g)
h = (2.4 m/s)² / (2 × 9.8 m/s²)
h = 0.294 m
The pendulum rises to a height of above the bottom. To determine the angle, we need to use trigonometry (see attached diagram).
L − h = L cos θ
cos θ = (L − h) / L
cos θ = (1.2 − 0.294) / 1.2
θ = 41.0°
Rounded to two significant figures, the pendulum makes a maximum angle of 41° with the vertical.
Answer: A.
Explanation: Roughly 180 - 200 million years ago, just before the first dinosaurs evolved. Mammals themselves evolved from a group or reptiles which exhibited mammal-like traits. One of them was specialized teeth. Reptiles tend to have teeth all the same shape. The mammal-like reptiles evolved tiny teeth in front of the jaw and two pairs of over sized fangs along the the sides. Like modern mammals, the head was large in proportion to the rest of the body. The jaws were also evolving another mammal trait, the ability to move sideways. Despite the lack of specialized teeth, acute hearing and the ability to chew, the dinosaurs evolved an adaptation which made them far more successful than mammals--modified leg bones. These limbs could be articulated directly under their bodies. This enabled the legs to support more weight, since the limbs were now under the body instead of at the sides. Then dinosaurs did something which secured their dominance for the next 120 million years - they began to stand on two legs. Although the back was still parallel to the ground, running on two legs greatly increased the dinosaur's speed. Mammals could simply not compete with swift, giant predators and were forced to remain small, and most became nocturnal to evade dinosaurs which were probably active during the day. Despite that they managed to survive which allowed the further evolution of mammals into us, humans.
Answer:
R = 5.28 103 km
Explanation:
The definition of density is
ρ = m / V
V = m /ρ
Where m is the mass and V the volume of the body
The volume of a sphere is
V = 4/3 π r³
Let's replace
4/3 π r³ = m / ρ
R =∛ ¾ m / ρ π
The mass of the planet is
M = 5.5 Me
R = ∛ ¾ 5.5 Me /ρ π
Let's reduce the density to SI units
ρ = 1.76 g / cm³ (1 kg / 10³ g) (10² cm / 1 m)³
ρ = 1.76 10³ kg / m³
Let's calculate
R = ∛ ¾ 5.5 5.97 10²⁴ / (1.76 10³ pi)
R = ∛ 0.14723 10²¹
R = 0.528 10⁷ m
R = 0.528 104 km
R = 5.28 103 km
The correct answer is D: which is none of the above.
Hint: a wreckling ball contains pontential energy that acts like a pendulum
a pot of water contains pontential thermal energy
