Consider three masses with m1 = 1 kg located at (0 ,0), m2 = 2kg located at (-1,1) and m3= 3kg located at(1, 1), all distances in meters. The x and y coordinates of the center of mass are
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
Consider three masses with m1 = 1 kg located at (0 ,0), m2 = 2kg located at (-1,1) and m3= 3kg located at(1, 1), all distances in meters. The x and y coordinates of the center of mass are
a. 1/5, 1b. 1/6, 1/6 c. -5/6, -1d. 1/6, 5/
2. Consider the two square plates below. The mass of the left plate is 2 kg, and the right plate is 1 kg. The plates are 20 cm and 40 cm on a side respectively. The origin is located at the lower left edge of the smaller plate. The y-position of the center of mass (in cm) is
a. 20/3b. 40/3c. 20d. 40
(0,0)
3. A mass 1 is located at (0,0), a mass 2 at (1,2) and mass 3 at (1,-2) all in meters. The moment of inertia about an axis out of the page through the origin is (in kg-m2)
a.25b.14c. 26 d. 25/3
4. A projectile of mass 0.5 kg moving with speed V = 100 m/s strikes and imbeds itself into a wooden block of mass 4.5 kg. The final kinetic energy of the system (in Joules) is closest to
a. 50 b. 1000 c. 250 d. 0
5. A 20 kg child stands at rest holding a 5 kg rock. He throws the rock forward with a velocity of 20 m/s. His recoil velocity is
a. -5b. -4c. 0d. 25
6. In a certain collision the initial momentum and kinetic energy of the system of colliding objects are respectively 400 kg-m/s and 1000 J. The final momentum and kinetic energy of the objects are 400 kg-m/s and 800 J. For this collision, what is correct?
a. this cannot happen because the momenta are equal b. the collision is inelastic
c. no energy was lost to heat and deformation d. the internal forces do not cancel pairwise.
7. Mass m1 = 5 kg moves to the right with speed v1 = 18 m/s. It strikes a second mass m2 = 4 kg moving away from it with a velocity v2 = 9 m/s. The final velocities of m1 and m2 are respectively (in m/s)
a. -21, -10 b. 0, 30 c. 10, 19 d. 10, 21.
8. A 500 kg vehicle travels with velocity V0 = 10 m/s i. It is struck in the rear by a car so that it then has a velocity of Vf = 12 m/s i. The impact takes 0.5 seconds. The average force acting on the vehicle (in Newtons) is
a.22000ib.10000ic. 5000jd. 2000i
9. The angular position of a point on the rim of a rotating wheel is given by . The
a. 20, 20 b. 18, 20 c. 18, 16 d. 20, 16
10. A wheel is rotating at an angular velocity of rad/s. It comes to rest after rotating 50 radians. The
a. -3/5b. -18c. -9d. 1500
11. A 10 kg sphere is rotating with an angular velocity of = 5 rad/s. It possesses a kinetic energy of 200 J. The radius of the sphere (in m) is
a. 1 b. 2 c. d. 25
12. Three forces, F1 = 5 N, F2 = 10 N and F3 = 15 N act on a disk of radius R = 2 m as indicated. F1 acts at the rim of the disk, F2 at 1m from the axis of rotation, and F3 through the axis as indicated. The magnitude (in N-m) of the torque about its center point is closest to (cw indicates clockwise and ccw counterclockwise)
a. 0b. 20 cwc. 20 ccw d. 30 cc
F3
F2
F1
13. An automobile moves down the street at speed v = 80 mph. The speed of a point at the top of the wheel and at bottom of the wheel as it rolls forward (in mph) are respectively
a. 80, 80 b. 160, 80 c. 160, 0 d. 0, 160
14. A cylinder with moment of inertia I = MR2/2 sits on a ramp of height H. The cylinder rolls without slipping to the bottom of the ramp. Conservation of energy for the cylinder as applied to this situation gives for its velocity at the bottom
15. A 4 kg object is moving with velocity (in m/s) r = 2 i + 3 j. The
a. -20 k b. -1 kc. 20kd. 4k
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