On the Newtonian theory of gravity, gravitation affects anything with mass. Assuming that none of the answer choices is the only thing that exists in the universe, all of the answer choices are subject to the law of universal gravitation (hence “universal”).
Satellites, water, frogs, and stars all have mass as they are all composed of matter. Thus, all four answer choices should be circled.
Answer:
The kinetic energy of the bullet is 5.4 × 10³ J
Explanation:
Hi there!
The equation of kinetic energy is the following:
KE = 1/2 · m · v²
Where:
KE = kinetic energy.
m = mass of the bullet.
v = speed of the bullet.
Let´s convert the mass unit to kg so that our result is in Joules:
64 g · ( 1 kg / 1000 g) = 0.064 kg
Then, the kinetic energy will be the following:
KE = 1/2 · 0.064 kg · (411 m/s)²
KE = 5.4 × 10³ J
Answer:
44.3 m/s
Explanation:
a) Draw a free body diagram of the mass M. There are three forces:
Weight force mg pulling down,
Normal force N pushing perpendicular to the ramp,
and tension force T pulling parallel up the ramp.
Sum of forces in the parallel direction:
∑F = ma
T − Mg sin 30° = 0
T = Mg sin 30°
T = Mg / 2
Draw a free body diagram of the hanging mass m. There are two forces:
Weight force mg pulling down,
and tension force T pulling up.
Sum of forces in the vertical direction:
∑F = ma
T − mg = 0
T = mg
Substitute:
mg = Mg / 2
m = M / 2
M = 2m
b) Velocity of a standing wave in a string is:
v = √(T / μ)
T = mg, and m = 5 kg, so T = (5 kg) (9.8 m/s²) = 49 N. Therefore:
v = √(49 N / 0.025 kg/m)
v = 44.3 m/s
