Mechanics Quiz for AP Physics B & C (page 2)

Answers

1. Weight is mg. So, mass is weight divided by g = 100 N/(10 N/kg) = 10 kg.
2. PE = mgh, gravitational potential energy;

PE = 1/2kx², potential energy of a spring.

3.  
   1. mg sin θ is parallel to the incline.
   2. mg cos θ is perpendicular to the incline.
4. The definition of work is work = force times parallel displacement

The work-energy principle states that net work = change in kinetic energy

5. vectors: acceleration, force, momentum, velocity, displacement

scalars: speed, work, mass, kinetic energy

6. Only forces acting on an object and that have a single, specific source can go on freebody diagrams. Some of the things that cannot go on a free-body diagram but that students often put there by mistake:

motion             mass             acceleration             ma

centripetal force             velocity             inertia

7. Impulse is force times time interval, and also change in momentum. Impulse has units either of Newton · seconds or kilogram · meters/second.
8. Momentum is conserved in all collisions. Kinetic energy is conserved only in elastic collisions.
9. Using the reasoning from question #1, if weight is mg, then m = W/g.
10. The acceleration of a projectile is always g; i.e., 10 m/s², downward. Even though the velocity is instantaneously zero, the velocity is still changing, so the acceleration is not zero. [By the way, the answer "–10 m/s²" is wrong unless you have clearly and specifically defined the down direction as negative for this problem.]
11. The magnitude of the resultant force is found by placing the component vectors tip-totail. This gives a right triangle, so the magnitude is given by the Pythagorean theorem, 50 N. The angle of the resultant force is found by taking the inverse tangent of the vertical component over the horizontal component, tan^–1(40/30). This gives the angle measured from the horizontal.
12. 

friction force divided by normal force μ has no units.

13. Acceleration is the slope of a velocity-time graph.
14. Displacement is the area under a velocity-time graph (i.e., the area between the graph and the horizontal axis).

Velocity is the slope of a position-time graph. If the position-time graph is curved, then instantaneous velocity is the slope of the tangent line to the graph.

15. Because acceleration is not zero, the object cannot be moving with constant speed. If the signs of acceleration and velocity are the same (here, if velocity is positive), the object is speeding up. If the signs of acceleration and velocity are different (here, if velocity is negative), the object is slowing down.
16. An object always moves in the direction indicated by the velocity.
17. Near the surface of a planet, mg gives the gravitational force. Newton's law of gravitation, Gmm/r², is valid everywhere in the universe. (It turns out that g can be found by calculating GM_planet/R_planet ², where R^planet is the planet's radius.)
18. An object in uniform circular motion experiences a centripetal, meaning "center seeking," force. This force must be directed to the center of the circle.
19. This and all three kinematics equations are valid only when acceleration is constant. So, for example, this equation can NOT be used to find the distance travelled by a mass attached to a spring. The spring force changes as the mass moves; thus, the acceleration of the mass is changing, and kinematics equations are not valid. (On a problem where kinematics equations aren't valid, conservation of energy usually is what you need.)