Mass M is divided into two parts xM and (1-x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum. Find this maximum value of x.

A constant force acts on a body of mass 0.9 kg at rest for 10s. If the body moves a distance of 250 m, the magnitude of the force is (1) 3 N (2) 3.5 N (3) 4.0 N (4) 4.5 N

The force acting on a particle is F - (10x – 17) N, where x is in meters. (a) Make a plot of this force versus x from x = 0 to x = 3.00 m. F (N) F (N) 20 50 40 10- 30 0,5 20 1.0 20 25 x (m) 30 -10 10 atx (m) 3.0 0.5 1.0 1.5 2.0 2.5 F (N) F (N) 0,5 1.0 1,5 2.0 2.5 x (m) 30 10 -10 -20 0,5 15 x (m) 30 10 2.5 -30 -10 -40 -50 -20 (b) From your graph, find the net work done by this force on the particle as it moves from x = 0 to x= 2.55 m. (Include the correct sign.)

*15-52. The free-rolling ramp has a mass of 40 kg. A 10-kg crate is released from rest at A and slides down 3.5 m to point B. If the surface of the ramp is smooth, determine the ramp's speed when the crate reaches B. Also, what is the velocity of the crate? 3.5 m 30° 00.

Determine the reaction force at point B 92.5 N 50 N 75 N 65.5 N 67.5 N 60 N 4m A 2 N/m 6 m 2m B 4m 80 N

(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.48 x 10 m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 x 10 m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 x 10 m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar…

A hockey puck with mass 0.1 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.2 N to the puck, parallel to the x-axis; she continues to apply this force until t = 2 5. (a) What is the speed of the puck at t = 2 s? Round your answer to 2 decimal places.

A fish of mass 1kg is lying still on an inclined plane at 3o degrees above the horizontal. the magnitude of the normal force exerted by the plane on the fish is.  0N 9.8N 8.5 N 4.9N

55-56. Ganymede, one of Jupiter's moons, is the largest moon in our solar system. It has a mass of 1.48 × 1023 kg and a radius of 2.63 × 10 m. A 15.0 kg lunar rover is on Ganymede's surface. 55. As the rover orbits Ganymede, it is observed that during a particular segment of time, its speed decreases. During this segment of time, the work done by gravity on the rover is: a positive b) negative c zero d) more info is needed to determine 56. Find Ganymede's escape speed (the minimum launch speed from Ganymede's surface such that the projectile never falls back). a) 2.39 km/s b) 2.74 km/s c) 3.09 km/s d) 3.44 km/s e) 3.79 km/s