(I) At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12.0 m/s2 A 24.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet, and (b) the weightof the brass ball on the Earth and on the planet?

(3.) A car of mass 2000 kg negotiates without slipping a banked curved road of radius 40 m with speed of 12 m/s. (Neglect friction) (a) Find the banked angle to accomplish this. (b) Find the Centerpital force

At what minimum speed must a roller coaster be traveling so that passen- gers upside down at the top of the circle (Fig. 5–48) do not fall out? Assume a radius of curvature of 8.6 m. FIGURE 5-48 Problem 73.

The Earth exerts a gravitational force on the Moon, keeping it in its orbit. The Newton third law partner to this force is O The centripetal force on the Moon. O The ocean tides due to the Moon and the Sun O The gravitational force on the Earth by the Moon. The nearly circular orbit of the Moon around the Earth.

angle with 1.00 m sides. Find the magnitude and direction of the resultant gravitational force on each particle. * 12 A spaceship of mass 1.0 × 106 kg is accelerated at a rate of 1.0 m/s² toward a binary star, which consists of two stars of equal mass m, as shown in Fig. 6-16. Find the mass m of each star. m M 1.0 × 106 kg x 1.5 X 1010 m 1.0 × 1010 m Fig. 6-16 I * 13 A particle of mass m is between a 1.00 × 10² kg mass and a 4.00 × 10² kg mass, which are 10.0 m apart. X a €

(c) The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.25 with the floor. If the train is initially moving at a speed of 48 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

A science-fiction tale describes an artificial “planet" in the form of a band completely encircling a sun (Fig. 5–50). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate livable), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days? Sun FIGURE 5-50 Problem 88.

(III) (a) Suppose the coefficient of kinetic friction between ma and the plane in Fig. 4-62 is µk = 0.15, and that mA = mB = 2.7 kg. As mB moves down, determine the magnitude of the acceleration of ma and mg, given 0 = 34°. (b) What smallest value of pk will keep the system from accelerating? [Ignore masses of the (frictionless) pulley and the cord.] mB FIGURE 4-62 Problem 67.

(II) A train locomotive is pulling two cars of the same mass behind it, Fig., 4–51. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car (Fr1), to that between the first car and the second car (Fr2), for any nonzero acceleration of the train. Car 2 Car 1 FIGURE 4–51 Problem 27.