Chapter N6 Linearly Constrained Motion N6B.1, B.4, B.5, S.1, S.8 Due Monday

Forces from motion  Implies  Three equations

Ex. What force is required to push a 50 kg cart with frictionless wheels up a 30 degree incline at constant speed?  How much more force is required to push a cart up an incline at constant speed than to hold it still?  The same force is required for both  Draw the free body diagram for the cart.  Draw the net force diagram for the cart.  Do the trig and write the acceleration equation(s).

Solution  As there is no acceleration, the sum of the forces is zero. θ θ mg mg cosθ mg sinθ F Hand =245 N

Friction forces  For static friction F f =μ s N This is what is necessary to “break the object loose” and get it moving  For kinetic friction F f =μ k N This is what is necessary to keep it moving.  The static friction is usually significantly higher than the kinetic friction.

Ex. What force is required to push a 50 kg cart with a μ k of.3 up a 30 degree incline at constant speed?  This problem is the same as we solved before except that we need to include F f.  Write the vector equation on your paper. F Hand =245 N N = N

Drag forces  The drag force of an object moving with a velocity v, through a fluid of density ρ, and cross-sectional area A is given by  Where C is a constant determined by the shape of the object. ( for a sphere C =.5)

Find the terminal velocity of a baseball in the atmosphere if it is dropped from a hovering helicopter C = 0.5 ρ = 1.29 kg/m 3 Radius = 7 cm A = π(.07 m) 2 =.0154 m 2 Mass of ball =.14 kg Terminal velocity of the ball = 16.8 m/s

Find the acceleration of a 50 kg cart with frictionless wheels rolling down a 30 degree incline.  Draw a free body diagram  Draw a net force diagram  Write the vector equations in column vector form a = 2.35 m/s 2

Find the acceleration of a cart with frictionless wheels rolling down a 30 degree incline. In this case ma=mgsinθ a=gsinθ a=9.8m/s 2 ·sin(30º)=4.9m/s 2

Find the acceleration of a 50 kg cart with coefficient of kinetic friction of 0.3 sliding down a 30 degree incline.  Draw a free body diagram  Draw a net force diagram  Write the vector equations in matrix a=2.35 m/s 2

Problems chapter N6  N6B.1, B.4, B.5, S.1, S.8  Due Monday

A rocket is shot straight into the air for 4 seconds with an acceleration of 20 m/s 2. Find the velocity with which it returns to the ground and the total time it spends in the air  Part 1: v 0 =0, z 0 =0, a=20 m/s 2, t=0 at t = 4 s, v= 80m/s, z=160m  Part 2: v 0 =80m/s, z 0 =160, a=-9.8 m/s 2 t=0 When v=0, t*=8.16 sec, z=468.5m  Part 3: v 0 =0, z 0 =468.5, a=-9.8 m/s 2 t=0 When z=0, v= 97.7 m/s, t=9.96s  The total time in the air t= 4s+8.16s+9.96s=22.1 seconds