2) Draw an x y axis and define the direction you are moving in as the + direction. If not moving, + direction is arbitrary
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1 Solving Dynamics Problems 1) Draw Sketch / FBD with all forces shown 2) Draw an x y axis and define the direction you are moving in as the + direction. If not moving, + direction is arbitrary 3) Write sin and cos equations for components of forces not acting the x o y direction. F cos θ, F sin θ 4) Setup F net equations in x and y directions F net(x) = ma x F net(y) = ma y *a = 0 if not moving in that direction or moving at constant velocity 5) Substitute variables of actual forces (F, Fsin θ, F n, F g etc) For F net(x) and F net(y) using proper +/ signs for directions. 6) Solve for missing thing Other equations of possible use Old kinematics equations v f = v i + at d = v i t + ½ at 2 etc F g =mg f = µf n (will learn later) 1
2 A) Four forces act on a 50 N object. F 1 =10N east, F 2 = 3.5 N north, F 3 = 4 N west, F 4 = 6N south. Determine the acceleration of this object. B A 100 kg rocket sled starts from rest and accelerates straight 100 m on a friction free surface to a final speed of 25 m/s. What is th engines force. 2
3 C) A man pulls a 10 kg box with a force of 150 N. 50 N of friction act on the box. Determine the (a) acceleration (b) normal force (c) velocity of the box after 2 seconds 3
4 D) A 25 kg box is pulled with an unknown force F directed at 60 degrees measured from the vertical and towards the right. 25 N of frictio force impede the blocks motion as it accelerates at 2 m/s 2 to the right on a flat surface. (a) What force is the box pulled with (b) What is the magnitude of the normal force 4
5 STUDENTS DO E) A 1000 kg elevator is lifted by a force of N N of friction impede the motion of the elevator. (a) What is the acceleration o the elevator? (b) How far does it move in 2 seconds if it starts from rest F) A 250 N box is pushed with a force of degrees below horizontal and the box moves at a constant speed. (a) Determine the friction force acting on the box (b) Determine the normal force acting on the box (c) Given the same friction force as found in part a, determine the acceleration of the box if the magnitude of the force acting was increased to 150 N. 5
6 Coefficient of Friction 6
7 Friction Problems 1.) You have a 75 kg mass. You run on the floor trip on a banana and go sliding into a pile of manure. The coefficient of kinetic friction i What is your acceleration? 2.) A 30 kg box rests on a surface. A 50 N force is applied acting to the right. The coefficient of static friction is 0.50 the coeff of kinetic is (a) What is the friction force acting on the box. (b) If 150 N of force was applied, how much friction acts on the box 7
8 STUDENTS DO 3.) A 98 N box is pushed horizontally with a force of degrees below horizontal and the box moves at a constant speed. Determine the coefficient of kinetic friction between the box and the surface 8
9 4.) A rock climber is supported between two nearby rock walls. The coefficient of static friction between his back and the wall is 0.60 and the coefficient of static friction between his shoes and the wall is If the climber has a mass of 70 kg and the friction of each surface is at a maximum, what force must the climber exert on the walls (normal force) to remain stationary? 9
10 Connected Objects systems of particles 10
11 6.) Two boxes are connected by a light cord and are resting on a flat frictionless table. The front box has a mass of 10 kg and the back box has a mass of 12 kg. A horizontal force of 40 N is applied to the 10 kg box and pulls to the right. Find the acceleration of each box and the tension in the cord. 11
12 5.) Two crates of mass 75 kg and 110 kg are in contact and at rest on a horizontal surface. A 730 N force is exerted on the 75 kg crate. I the coefficient of kinetic friction is 0.15, calculate (a) the acceleration of the system, and (b) the force that each crate exerts on the other 12
13 STUDENTS DO 7.) One 3 kg paint bucket is hanging by a massless cord. A second cord is attached underneath that bucket and a second 3 kg paint bu is attached to it. (a) If the buckets are at rest, what is the tension in each cord. (b) If the buckets are pulled upward and accelerate at constant 1.6 m/s 2, what is the tension in each cord. 13
14 8.) A 1150 kg elevator is suspended by a wire which is drawn over a pulley and attached to a 1000 kg counter weight on the other side of the wire. What is the acceleration of the elevator in this configuration and what is the tension in the wire 14
15 STUDENTS DO 9.) A 5 kg box on a flat table is connected to a 2 kg box by a cord. The cord is placed over a pulley that is attached to the edge of the ta and the 2 kg box hangs over the edge of the table pulling the 5 kg box towards the edge of the table. The coefficient of kinetic friction between the box and the table is 0.20 (a) Determine the acceleration of each block and (b) the tension in the rope. (c) Determine the coefficient of static friction that would be necessary in order to keep the system at rest. 15
16 16
17 INCLINES 17
18 Newtons Laws Student Sheet 7 1.) Draw the x and y components of the weight TO SCALE for the inclines below 2.) Based on your drawings above, answer the following What happens to the Normal Force acting on a box when you increase the incline? Assuming that the box does not move, what happens to the friction force when you increase the incline? Which component of the weight causes the box to accelerate? Based on this picture below, answer the following 18
19 kinetic friction and inclines 19
20 11.) A 1 kg box slides down a 30 degree incline and accelerates at 1.2 m/s 2. What is the coefficient of kinetic friction on this incline? 20
21 STUDENT DO 12.) A 98.1 N box is pushed up a 60 degree incline with a force of N directed parallel to the incline surface. The coefficient of kinetic friction between the box and the ramp is 0.5. If the box starts from rest, how fast will it be moving when it reaches the top of the 5 m long incline? 21
22 13.) Block m 1 is placed on an inclined plane of angle θ with coefficients of friction μ s and μ k. Block m 2 is tied to block m 1 with a rope, and block m 2 is hung over the side of the incline as shown below. Both blocks have equal masses (m 1 =m 2 =m) (a) Draw a FBD of each box and the incline and state your reasoning for the direction of the friction force. (b) Derive a formula in terms of θ to calculate the minimum u s needed to keep the system at rest. (c) assume u s on the incline is less than the minimum amount as described In terms of μ k, θ and g, derive a formula for the acceleration of the system. 22
23 STUDENTS DO 14) 2000B2. Blocks 1 and 2 of masses m l and m 2, respectively, are connected by a light string, as shown above. These blocks are further connected to a block of mass M by another light string that passes over a pulley of negligible mass and friction. Blocks l and 2 move with constant velocity v down the inclined plane, which makes an angle θ with the horizontal. The kinetic frictional force on block 1 is f and that block 2 is 2f. a. On the figure below, draw and label all the forces on block m l. Express your answers to each of the following in terms of m l, m 2, g, θ, and f. b. Determine the coefficient of kinetic friction between the inclined plane and block 1. c. Determine the value of the suspended mass M that allows blocks 1 and 2 to move with constant velocity down the plane. d. The string between blocks 1 and 2 is now cut. Determine the acceleration of block 1 while it is on the inclined plane. 23
24 24
25 Elevator Problems 25
26 Tension and Pulleys 26
27 27
28 28
29 29
30 WORKING WITH PULLEYS 30
31 31
32 Real Life Ropes 32
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