# Chapter 6 - Force and Motion II Chapter 6 Force and Motion II Fall 2009 Review of chapter 5 Force and Motion I I. Newtons first law. II. Newtons second law. III. Particular forces: - Gravitational - Weight - Normal - Tension IV. Newtons third law. In the figure below, mblock=8.5kg and =30. Find (a) Tension in the cord. (b) Normal force acting on the block. (c) If the cord is cut, find the magnitude of the blocks acceleration. y N

T x Fg (a ) a 0 Fgx mg sin 30 (8.5kg )(9.8m / s 2 )0.5 41.65N (b) N Fgy mg cos sin 30 72.14 N (c) T 0 Fgx ma 41.65 N 8.5a a 4.9m / s 2 Chapter 6 Force and Motion II I. Frictional forces. II. Drag forces and terminal speed. III. Uniform circular motion. I. Frictional force Counter force that appears when an external force tends to slide a body along a surface. It is directed parallel to the surface and opposite to the sliding motion. Static: (fs) compensates the applied force, the body does -Static:

not move. f s F// Kinetic: (fk) appears after a large enough external force is -Kinetic: applied and the body loses its intimate contact with the surface, sliding along it. F (applied force) No motion Acceleration Constant velocity f k f s ,max f s , max s N If F// f s ,max body slides Friction coefficients

f k k N After the body starts sliding, fk decreases. decreases II. Drag force and terminal speed -Fluid: anything that can flow. Example: gas, liquid. -Drag force: D - Appears when there is a relative velocity between a fluid and a body. the relative motion of a body in a fluid. - Opposes - Points in the direction in which the fluid flows. Assumptions: * Fluid = air. * Body is baseball. * Fast relative motion turbulent air. 1 D CAv 2 2 C = drag coefficient (0.4-1). = air density (mass/volume).

A= effective bodys cross sectional area area perpendicular to v -Terminal speed: vt - Reached when the acceleration of an object that experiences a vertical movement through the air becomes zero Fg=D 1 D Fg ma if a 0 CAv 2 Fg 0 2 vt 2 Fg CA III. Uniform circular motion -Centripetal acceleration: v2 a r v, a are constant, but direction changes during motion. motion A centripetal force accelerates a body by changing the direction of the

bodys velocity without changing its speed. -Centripetal force: v2 F m R a, F are directed toward the center of curvature of the particles path. A puck of mass m slides on a frictionless table while attached to a hanging cylinder of mass M by a cord through a hole in the table. What speed keeps the cylinder at rest? N T mg T For M T Mg Mg

v2 v2 Mgr For m T m Mg m v r r m Calculate the drag force on a missile 53 cm in diameter ruising with a speed of 250 m/s at low altitude, where the ensity of air is 1.2 kg/m3. Assume C=0.75 1 2 D CAv 2 0.5 0.75 (1.2kg / m3 ) (0.53m / 2) 2 250m / s 6.2kN 2 The terminal speed of a ski diver is 160 km/h in the spread eagle position and 310 km/h in the nosedive position. Assuming that the divers drag coefficient C does not change from one point to another, find the ratio of the effective cross sectional area A in the slower position to that of the faster position.

2 Fg 2 Fg CAE AD 160km / h AE vt 3.7 CA 310km / h AD 2 Fg AE CAD Two blocks of weights 3.6N and 7.2N, are connected by a massless string and slide down a 30 inclined plane. The coefficient of kinetic friction between the lighter block and the plane is 0.10; that

between the heavier block and the plane is 0.20. Assuming that the lighter block leads, find (a) the magnitude of the acceleration of the blocks and (b) the tension in the string. Mo Block A NA NB T FgxA Block B fkA FgyA Light block A leads FgxB fkB

T FgyB nt e m ve NB fk,A NA T T A FgA fk,B B

FgB Light block A leads a 3.49m / s 2 T 0.2 N Block B weighs 711N. The coefficient of static friction between the block and the table is 0.25; assume that the cord between B and the knot is N horizontal. Find the maximum weight T2 of block A for which the system will f be stationary. T1 T1 T3 T3 System stationary f s ,max s N FgB

FgA Block B N mB g T1 f s ,max 0 T1 0.25 711N 177.75 N 177.75 N Knot T1 T2 x T2 cos 30 T2 205.25 N cos 30 T2 y T2 sin 30 T3 Block A T3 m A g T2 sin 30 0.5 205.25 N 102.62 N Blocks A and B have weights of 44N and 22N, respectively. (a) Determine the minimum weight of block C to keep A from P sliding if s between A and the table is 0.2. (b) Block C suddenly is lifted of A. What is the acceleration of block A if k between A and the table is 0.15? (a) f f s ,max s N

Block A a 0 T f s ,max 0 T s N (1) N f T Block B T mg 0 T 22 N Wc (2) WA=44N T WB=22N T 22 N (1) ( 2) N

110 N s 0.2 Blocks A, B N WA WC WC 110 N 44 N 66 N Blocks A and B have weights of 44N and 22N, respectively. (a) Determine the minimum weight of block C to keep A from P sliding if s between A and the table is 0.2. (b) Block C suddenly is lifted of A. What is the acceleration of block A if k between A and the table is 0.15? C disappears N m A g 44 N (b) T k N m A a T mB g mB a N f

T Wc WA=44N T WB=22N T 6.6 4.5a T 22 2.2a a 2.3m / s 2 T 17 N The two blocks (with m=16kg and m=88kg) shown in the figure below are not attached. The coefficient of static friction between the blocks is: s=0.38 but the surface beneath the larger block is frictionless. What is the minimum value of the N f horizontal force F required to keep the N N smaller block from slipping down the larger block?

mg Mg Movement Fmin required to keep m from sliding down? Treat both blocks as a single system sliding across a frictionless floor F F mtotal a a mM F Small block F N ma m mM f s mg 0 s N mg 0 (1) ( 2) (1) ( 2) mg m M F s M

mg F 488 N s M mM An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 5 kN, and the radius of the circle is 10 m. What are the magnitude and the direction of the force of the boom on the car at the top of the circle if the cars speed is (a) 5m/s (b) mg m/s? 12 The force of the boom on the car is capable of pointing any direction v2 v2 FB W 1 FB W m

R Rg (a) v 5m / s FB 3.7 N up y FB W (b) v 12m / s FB 2.3 down