Chapter 5 physics

The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?

1.6*10^11 m

Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1.74×106m and its mass is 7.35×1022kg

1.62 m/s^2

A bucket of mass 2.50 kg is whirled in a vertical circle of radius 1.50 m . At the lowest point of its motion the tension in the rope supporting the bucket is 33.0 N . Find the speed of the bucket.

2.26 m/s

The Sun rotates around the center of the Milky Way Galaxy (the figure below (Figure 1) ) at a distance of about 30,000 light-years from the center (1ly=9.5×1015m). If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere.

3.5*10^41 kg

A bucket of mass 2.50 kg is whirled in a vertical circle of radius 1.50 m . At the lowest point of its motion the tension in the rope supporting the bucket is 33.0 N . How fast must the bucket move at the top of the circle so that the rope does not go slack?

3.83 m/s

The space shuttle releases a satellite into a circular orbit 735 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?

7.48*10^3 m

If you weigh 660 N on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 21.0 km ? Take the mass of the sun to be ms = 1.99×1030 kg , the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 , and the acceleration due to gravity at the earth's surface to be g = 9.810 m/s2 . Express your weight wstar in newtons.

8.10X10^23 N

Two identical satellites orbit the earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v. At what distance from the center of the earth does the second satellite orbit?

At a distance greater than r.

Earth's orbit around the Sun is slightly elliptical. Thus, Earth actually gets closer to the Sun during part of the year. What happens to Earth's orbital speed when it is closer to the Sun?

Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun

Now assume that two identical cars of mass m drive along a highway. One car approaches a curve of radius 2R at speed v. The second car approaches a curve of radius 6R at a speed of 3v. How does the magnitude F1 of the net force exerted on the first car compare to the magnitude F2 of the net force exerted on the second car?

F1=13F2

Derive a formula for the mass of a planet in terms of its radius r, the acceleration due to gravity at its surface gP, and the gravitational constant G.

MPlanet = (gP*r^2)/G

Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change?

The gravitational force increases by a factor of 4.

An object moves in a circular path at a constant speed. What is the direction of the net force acting on the object?

The net force is directed toward the center of the circular path

An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors?

The velocity and acceleration vectors are perpendicular.

Why does a satellite in a circular orbit travel at a constant speed?

There is no component of force acting along the direction of motion of the satellite.

Now assume that a satellite of mass m is orbiting the earth at a distance r from the center of the earth with speed ve. An identical satellite is orbiting the moon at the same distance with a speed vm. How does the time Tm it takes the satellite circling the moon to make one revolution compare to the time Te it takes the satellite orbiting the earth to make one revolution?

Tm is greater than Te.

At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?

r = 3.46×108 m

A small car of mass m and a large car of mass 4m drive along a highway at constant speed. They approach a curve of radius R. Both cars maintain the same acceleration a as they travel around the curve. How does the speed of the small car vS compare to the speed of the large car vL as they round the curve?

vS=vL

A curve of radius 64 m is banked for a design speed of 125 km/h . If the coefficient of static friction is 0.34 (wet pavement), at what range of speeds can a car safely handle the curve?

vmin, vmax = 88,230 km/h