Space Shuttle launch The mass of the Space Shuttle at launch was about 2 .1 × 10 6 kg . Much of this mass was the fuel used to move the orbiter, which carried the astronauts and various items in the shuttle’s payload. The Space Shuttle generally traveled from 3 .2 × 10 5 m ( 200 mi ) to6 .2 × 10 5 m (385 mi) above Earth’s surface. The shuttle’s two solid fuel boosters (the cylinders on the sides of the shuttle) provided 71.4% of the thrust during liftoff and the first stage of ascent before being released from the shuttle 132 s after launch at 48,000 m above sea level. The boosters continued moving up in free fall to an altitude of approximately 70,000 m and then fell toward the ocean to be recovered 230 km from the launch site. The shuttle’s five engines together provided 3 .46 × 10 7 N of thrust during liftoff. What answer below is closest to the speed of the shuttle and boosters when they were released? Assume that the free-fall gravitational acceleration at this elevation is about 9 .6 m/s 2 down. a. 100 m/s b. 300 m/s c. 600 m/s d. 1000 m/s
Space Shuttle launch The mass of the Space Shuttle at launch was about 2 .1 × 10 6 kg . Much of this mass was the fuel used to move the orbiter, which carried the astronauts and various items in the shuttle’s payload. The Space Shuttle generally traveled from 3 .2 × 10 5 m ( 200 mi ) to6 .2 × 10 5 m (385 mi) above Earth’s surface. The shuttle’s two solid fuel boosters (the cylinders on the sides of the shuttle) provided 71.4% of the thrust during liftoff and the first stage of ascent before being released from the shuttle 132 s after launch at 48,000 m above sea level. The boosters continued moving up in free fall to an altitude of approximately 70,000 m and then fell toward the ocean to be recovered 230 km from the launch site. The shuttle’s five engines together provided 3 .46 × 10 7 N of thrust during liftoff. What answer below is closest to the speed of the shuttle and boosters when they were released? Assume that the free-fall gravitational acceleration at this elevation is about 9 .6 m/s 2 down. a. 100 m/s b. 300 m/s c. 600 m/s d. 1000 m/s
Space Shuttle launch The mass of the Space Shuttle at launch was about
2
.1
×
10
6
kg
. Much of this mass was the fuel used to move the orbiter, which carried the astronauts and various items in the shuttle’s payload. The Space Shuttle generally traveled from
3
.2
×
10
5
m
(
200 mi
)
to6
.2
×
10
5
m
(385 mi) above Earth’s surface. The shuttle’s two solid fuel boosters (the cylinders on the sides of the shuttle) provided 71.4% of the thrust during liftoff and the first stage of ascent before being released from the shuttle 132 s after launch at 48,000 m above sea level. The boosters continued moving up in free fall to an altitude of approximately 70,000 m and then fell toward the ocean to be recovered 230 km from the launch site. The shuttle’s five engines together provided
3
.46
×
10
7
N
of thrust during liftoff.
What answer below is closest to the speed of the shuttle and boosters when they were released? Assume that the free-fall gravitational acceleration at this elevation is about
9
.6 m/s
2
down.
EXCEL Spring Problem:
An experiment is conducted to determine the value of a spring constant. Objects of varied mass are suspended from the spring and the spring deflections are measured. The results are as follows:
Mass, m (kg)
Deflection, x (mm)
5.3
15
7.1
22
10.2
31
12
38
15.4
45
Use EXCEL to determine the spring constant, k, in N/m.
calculate the energy required to send a 1 kg object from the surface of Earth to the satellite located 42.16*10^6m from the center of the Earth. Assume the location from which the object is being launched is 6.37*10^6m from the center.
a. Use the object's weight at the surface of the earth (g=9.8) to find Newton's proportional constant k for this object.
b. Write a definite integral that calculates the energy required to send the object to orbit, then use the Fundamental theorem of calculus to calculate the energy.
c. Write t he formula for a Reimann sum that is guaranteed to estimate the energy required to send the object to orbit, accurate with 10^5 J.
d. calculate the fraction of the object's total distance traveled at which half of the total required energy is expended.
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=2.93×106 g/m3 and volume ?=1.94×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10-11 N·m2/kg2 .vesc = ? m/s
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