AP Mechanics Summer Assignment

Transcription

1 AP Mechanics Summer Assignment To be completed in summer Submit for grade in September Name: Date:

2 Equations: Kinematics (For #1 and #2 questions: use following equations only. Need to show derivation before using other equations, such as those for R and H) v f = v i + at v avg = (v i + v f )/ 2 x f = v i *t + ½ a*t 2 v f 2 = v i 2 + 2a*x Newton s 2 nd Law F = ma f = N F c = mv 2 /r Energy and Work K i + U i = K f + U f K = ½ mv 2 U g = mgh U s = ½ kx 2 conservation of energy Linear momentum P i = P f p = mv conservation of momentum Rotation = r * F * sin Translational equilibrium: F i = 0 Rotational equilibrium: i = 0

3 Do not use calculator. Show all work. 1. This question concerns the motion of a car on a straight track. The car s velocity as a function of time is plotted below: a) Describe what happened to the car at time t = 1s. v (m/s) t (s) b) How does the car s average velocity between time t = 0s and t = 1 s compare to its average velocity between times t = 1 s and t = 5 s? c) What is the displacement of the car from time t = 0 to time t = 7 s? And from t = 1 s to 6 s? (Note: displacement = area between the graph and the t axis) d) Plot the car s acceleration a during the time showed in figure above as a function of time. a (m/s 2 ) t (s) e) Make a sketch of the object s position as a function of time, assuming that the car begins at x = 0. x (m) t (s)

4 2. Consider a projectile moving in a parabolic trajectory under constant gravitational acceleration. Its initial velocity has magnitude v 0, and its launch angle with the horizontal is 0. Show all work when answering following questions. H a) Find the maximum height, H, of the projectile. h R b) Find the horizontal range, R, of the projectile. c) For what value of 0 will the range be maximized? d) If 0 < h < H, compute the time that elapses between passing through the horizontal line of height h in both directions (ascending and descending); that is, compute the time required for the projectile to pass through the two points shown in this figure.

5 Newton s Laws 3. This question concerns the motion of a crate being pulled across a horizontal floor by a rope. In the diagram below, the mass of the crate is m, the coefficient of kinetic friction between the crate and the floor is, and the tension in the rope is T. The rope forms an angle of with the horizontal surface. a) Draw and label all of the forces acting on the crate. (Do not draw components of the forces). T m b) Compute the normal force N acting on the crate in terms of m, T,, and g. c) Compute the friction f acting on the block in terms of m, T,,, and g. d) Compute the acceleration a of the crate in terms of m, T,,, and g.

6 Energy and work 4. A box of mass m is released from rest at point A, the top of a long, frictionless slide. Point A is at height H above the level of points B and C. Although the slide is frictionless, the horizontal surface from point B to C is not. The coefficient of kinetic friction between the box and this surface is k, and the horizontal distance between point B and C is x. H A m a) Find the speed of the box when it reaches point B. B x C b) Determine the value of k so that the box comes to rest at point C.

7 Linear Momentum (& circular motion) 5. A steel ball of mass m is attached to a light cord of length L and released when the cord is horizontal. At the bottom of its path, the ball strikes a block of mass M = 4m, initially at rest on a frictionless surface. At collision, the ball is detached from the cord and stick to the block. a) Find the speed of the ball right before it collides with the block. m L M b) Find the tension of the cord right before the ball collides with the block. c) Find the speed of the ball and the block right after the ball collides with the block.

8 6 A ladder of mass m is leaned again a wall as shown, forming an angle with the floor. The contact between the wall and the ladder is frictionless. There is friction between the ladder and the floor. The ladder is L meter long and its mass is uniformly distributed, so gravity acts at the center of the ladder. a) In the figure at right, draw and label all the forces acting on the ladder. (Do not draw force components.) b) The ladder is not moving, so it is in static equilibrium. Find the magnitude of the normal force acting on the ladder by the floor. c) Find the magnitude of the normal force acting on the ladder by the wall. d) Find the magnitude of the friction between the ladder and the floor.