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Magazine Problem 24
A car drives around a curve with radius \(410 \mathrm{m}\) at a speed of $32
\mathrm{m} / \mathrm{s} .$ The road is not banked. The mass of the car is
\(1400 \mathrm{kg} .\) (a) What is the frictional force on the car?
(b) Does the frictional force necessarily have magnitude $\mu_{\mathrm{s}} N
?$ Explain.
Problem 25
A car drives around a curve with radius \(410 \mathrm{m}\) at a speed of $32
\mathrm{m} / \mathrm{s} .\( The road is banked at \)5.0^{\circ} .$ The mass of
the car is \(1400 \mathrm{kg}\). (a) What is the frictional force on the car?
(b) At what speed could you drive around this curve so that the force of
friction is zero?
Problem 26
A curve in a stretch of highway has radius \(R\). The road is banked at angle
\(\theta\) to the horizontal. The coefficient of static friction between the
tires and road is \(\mu_{\mathrm{s}} .\) What is the fastest speed that a car
can travel through the curve?
Problem 27
An airplane is flying at constant speed \(v\) in a horizontal circle of radius \(r\). The lift force on the wings due to the air is perpendicular to the wings. At what angle to the vertical must the wings be banked to fly in this circle?
Problem 28
A road with a radius of \(75.0 \mathrm{m}\) is banked so that a car can navigate the curve at a speed of \(15.0 \mathrm{m} / \mathrm{s}\) without any friction. When a car is going \(20.0 \mathrm{m} / \mathrm{s}\) on this curve, what minimum coefficient of static friction is needed if the car is to navigate the curve without slipping?
Problem 29
What is the average linear speed of the Earth about the Sun?
Problem 30
The orbital speed of Earth about the Sun is $3.0 \times 10^{4} \mathrm{m} /
\mathrm{s}\( and its distance from the Sun is \)1.5 \times 10^{11} \mathrm{m}$.
The mass of Earth is approximately \(6.0 \times 10^{24} \mathrm{kg}\) and that
of the Sun is \(2.0 \times 10^{30} \mathrm{kg} .\) What is the magnitude of the
force exerted by the Sun on Earth? \([\) Hint: Two different methods are
possible. Try both.\(]\)
Problem 31
Two satellites are in circular orbits around Jupiter. One, with orbital radius
\(r,\) makes one revolution every \(16 \mathrm{h}\) The other satellite has
orbital radius \(4.0 r .\) How long does the second satellite take to make one
revolution around Jupiter?
Problem 33
Io, one of Jupiter's satellites, has an orbital period of 1.77 d. Europa,
another of Jupiter's satellites, has an orbital period of about 3.54 d. Both
moons have nearly circular orbits. Use Kepler's third law to find the distance
of each satellite from Jupiter's center. Jupiter's mass is $1.9 \times 10^{27}
\mathrm{kg}$
Problem 34
A spy satellite is in circular orbit around Earth. It makes one revolution in
\(6.00 \mathrm{h}\). (a) How high above Earth's surface is the satellite? (b)
What is the satellite's acceleration?
