*.58 The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star as we see it. As the star and planet orbit the center of mass of the star-planet system, the star moves toward and away from us with what is called the line of sight velocity, a motion that can be de- tected. Figure 13-49 shows a graph of the line of sight velocity ver- sus time for the star 14 Herculis. The star's mass is believed to be 0.90 of the mass of our Sun. Assume that only one planet orbits the star and that our view is along the plane of the orbit. Then approxi- mate (a) the planet's mass in terms of Jupiter's mass m, and (b) the planet's orbital radius in terms of Earth's orbital radius rE. 70 -70 1500 days Time Line of sight veloxity (m/s)

Show that the linear system obtained by adding a multiple of an equation in (2) to another equation is equivalent to (2).

1) Imagine rolling four objects are placed in a row at the same height at the top of an inclined plane and are released at the same time. The objects are uniform solid and thin hollow spheres, and solid and thin hollow cylinders that have same masses and radii. Rank the four objects from fastest (shortest time) down the inclined plane to the slowest. You might have learned that when dropped straight down, all objects fall at the same rate regardless of how heavy they are (neglecting air resistance). Is the same true for objects rolling down an inclined plane? Please explain, why?

12–125. The car travels around the circular track having a radius of r = 300 m such that when it is at point A it has a velocity of 5 m/s, which is increasing at the rate of i = (0.061) m/s², where t is in seconds. Determine the magnitudes of its velocity and acceleration when it has traveled one-third the way around the track. 12–126. The car travels around the portion of a circular track having a radius of r= 500 ft such that when it is at point A it has a velocity of 2 ft/s, which is increasing at the rate of i = (0.0021) ft/s², where t is in seconds. Determine the magnitudes of its velocity and acceleration when it has traveled three-fourths the way around the track.

WITH FRICTION Find minimum and maximum mass of ml to maintain the system in state of equilibrium; at rest. Given: m2= 3kg m3=10kg m4=18.7kg M3 Ms=0.2 90₁ = 20° MK = 0.1 M. M₂ Ms=0.2 Mk = 0.1 Ms=0.2 MK = 0.1 0₂-30

3) Two beads A and B of masses m and 2m respectively are free to slide in a vertical plane round a smooth circular wire of radius a and centre O. The bead A is at rest at the lowest point C of the wire while B is released from rest at a point on the same level as O. If the coefficient of restitution between the beads is, find the heights above C to which each particle rises after impact.

(I) In a ballistic pendulum experiment, projectile 1 resultsin a maximum height h of the pendulum equal to 2.6 cm.A second projectile (of the same mass) causes the pendulumto swing twice as high h2=5.2 cm, The second projectilewas how many times faster than the first?

A 2.00-kg object hangs, at rest, on a 1.00-m-long string attached to the ceiling. A 100-g mass is fired with a speed of 20 m/s at the 2.00-kg mass, and the 100.00-g mass collides perfectly elastically with the 2.00-kg mass. Write an equation for the motion of the hanging mass after the collision. Assume air resistance is negligible.

Two identical particles, each of mass 1 000 kg, are coasting in free space along the same path, one in front of the other by 20.0 m. At the instant their separation distance has this value, each particle has precisely the same velocity of 800 m/s. What are their precise velocities when they are 2.00 m apart? Figure P13 74