The attractive force F (in newtons, N) between two objects varies directly with the product of the masses of the objects (in kg) and inversely with the square of the distance between them (in meters). The Earth has a mass of 5.97 ×1024 kg; the Moon has a mass of 7.35 ×1022 kg; the distance between them is about 3.84 ×108 meters; and they exert a gravitational force on each other of about 1.98 ×1020 newtons. The distance between Earth and Mars is 5.46 ×1010 meters at minimum, and Mars has a mass of about 6.42 ×1023 kg. What is the gravitational force that the Earth and Mars exert on each other when they are closest to one another?

A. about 11.43 × 1016 newtons
B. about 11.88 × 1016 newtons
C. about 9.3 × 1016 newtons
D. about 8.55 × 1016 newtons

When a 5.0kg cart undergoes a 2.2m/s increase in speed, what is the impulse of the cart

Part f - example: finding two forces (part i) two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. the block in (figure 1) has a mass m=10kg and is being pulled by a force f on a table with coefficient of static friction îľs=0.3. four forces act on it: the applied force f (directed î¸=30â above the horizontal). the force of gravity fg=mg (directly down, where g=9.8m/s2). the normal force n (directly up). the force of static friction fs (directly left, opposing any potential motion). if we want to find the size of the force necessary to just barely overcome static friction (in which case fs=îľsn), we use the condition that the sum of the forces in both directions must be 0. using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: fcosî¸â’îľsn=0 fsinî¸+nâ’mg=0 in order to find the magnitude of force f, we have to solve a system of two equations with both f and the normal force n unknown. use the methods we have learned to find an expression for f in terms of m, g, î¸, and îľs (no n).

Mutt and jeff are running along a path each pushing a cart loaded with rocks. if mutt's wagon has a mass two times greater than jeff's and they want to stay together, arriving at their destination at the same time, what must happen? a) jeff should slow down so mutt can catch up. b) mutt must use half as much force to push his cart. c) mutt must use twice as much force to push his cart. d) mutt and jeff will use the same force, but mutt will take bigger steps.