1. An asteroid is simply a very large chunk of rock wandering through space. Between Mars and Jupiter, a large number of these asteroids orbit the Sun and form what is known as the Asteroid Belt. In the figure below left, three asteroids are shown which are very far from any other object of significant mass. Asteroids A, B, and C have masses M_A = 2.57 × 10⁹ kg, M_B = 6.75 × 10¹⁰ kg, and M_C = 1.26 × 10¹² kg respectively. At the instant show below, Asteroid B is a distance r₁ = 5.00 km from Asteroid A, and Asteroid C is a distance r₂ = 13.5 km from Asteroid A. The given angles are θ = 42.5° and φ = 28.8°. Determine the magnitude and direction of the net force on Asteroid A. Determine the direction and magnitude of its acceleration at the instant shown.
   
   

2. If you swing a bucket full of water fast enough in a vertical circle, the water will not fall out of the bucket at the top of the circle and drench you. How fast (in revolutions per minute) must the bucket be going, if the radius of the circle is 1.25 m? Hint: treat the water as a solid.
   
   

3. In the diagram below, a 2.5 kg block is being pressed against a wall by a force F which has magnitude 75 N at an angle θ = 30° as shown. The kinetic coefficient of friction between the block and the wall is μ_k = 0.15. Find the acceleration of the book.
   
   

4. Mars has mass 6.42 × 10²³ kg and radius 3393 km. What is the acceleration due to gravity on Mars? What is weight of a 70-kg person on Mars? If the same person is in a Martian elevator, what would have to be the direction and magnitude of the elevator's acceleration such that the person would have an apparent weight equal to that which the person would have on earth, i.e. W = mg_earth?
   
   

5. In the diagram below, a mass M = 15.0 kg is hung by strings in an elevator. The elevator is accelerating upwards at 2.00 m/s². Find the tension in each of the three strings. The angles in the diagram are θ = 41.0° and φ = 57.0°.
   
   
6. Not believing his Physics instructor, a student goes for a ride in a Ferris Wheel at an amusement park taking a weigh scale with him. He stands on the scale while his seat goes around on the circular ride. At the top of the ride, the 75.0-kg student finds that he "weighs" only 715 N.
   (a) If the Ferris Wheel has a radius of 12.7 m, find its speed.
   (b) What would the reading on the scale at the bottom of the ride?
   

Formulas

Kinematics

		vaverage = ½(vf+v0)
Δx = vaveraget	Δx = v0t + ½at2	v = v0 + at
		g = 9.81 m/s2

Newton's Laws

ΣFx = max	ΣFy = may	fmax static = μsN	fkinetic = μkN
G = 6.672 × 10-11 N-m2/kg2

Quadratic Formula

if ax²+bx+c = 0, then

Questions? mike.coombes@kpu.ca