Newton’s Laws of Motion and Free Body Analysis

1. M1= 2.5kg and M2=3.5kg An external force F= 12 Newtons is applied to m1. Calculate (a) the acceleration of the system, and (b) the tension force between m1 and m2. a)2.0m/s/s b) 7.0 N See Example 4.3.

2. A Block of mass 0. 50 kg travels with a speed of 2 2. A Block of mass 0.50 kg travels with a speed of 2.0 m/s in the positive x direction on a flat frictionless surface. On passing through the origin, the block experiences a constant force of 3.0 newtons, at a 60 deg angle relative to the x axis for 1.50 seconds. Calculate the velocity of the block at the end of this time. V=(6.5m/s)i+(7.8m/s)j A force is applied to a moving block when it reaches the origin, and the block then begins to deviate from its straight-line path. See Example 4.4.

3. If m1=5.0kg, m2=1.5 kg, and theta is 20 degrees, what is the acceleration of the system. Make your own free body diagram for M2 and assume no friction. 0.32 m/s/s

Static and Kinetic Friction (a) In the static region of the graph, as the applied force F increases, so does fs, that is, fs = F and fs < μsN. (b) When the applied force F exceeds fsmax = μsN, the heavy file cabinet is set into motion. (c) Once the cabinet is moving, the frictional force decreases, since kinetic friction is less than static friction (fk < fsmax). Thus, if the applied force is maintained, there is a net force, and the cabinet is accelerated. For the cabinet to move with constant velocity, the applied force must be reduced to equal the kinetic friction force: fk = μk N.

Table 4.1 Approximate Values for Coefficients of Static and Kinetic Friction between Certain Surfaces

4. If the coefficient of static friction is between the 40 kg crate and the floor is 0.065. What is the magnitude of the horizontal applied force the worker must apply to keep the crate moving? If the worker maintains that force once the crate moves and the coefficient of kinetic friction is 0.500, what is the magnitude of the acceleration of the crate? 1.48 m/s/s See Example 4.10.

A crate sits in the middle of a flat bed truck that is traveling at 80 km/hr on a level road. The coefficient of static friction between the crate and the truck is 0.40. What is the minimum stopping distance for the truck if the crate is not to slide? 62m See Example 4.12.

5. If the coefficient of friction is 0 5. If the coefficient of friction is 0.560, what should be the value of m3 if the system is not to accelerate? Given m1=0.150kg, m2=0.250 kg. if m3=0.100 kg, what is the acceleration of the system? 0.179 kg, 0.862 m/s/s Exercises 72, 110, and 111

6. The Atwood’s machine was invented by British scientist George Atwood to study motion . If m1=0.55 kg and M2=0.80 kg, calculate the acceleration of the system, and the tension in the string. 1.8m/s/s, 6.4 N Exercises 80, 81, and 82

7. In the frictionless system shown below (m1=2 7. In the frictionless system shown below (m1=2.0 kg), what is mass m2, if the system is to remain at rest? 1.2 kg Exercises 84, 85, and 112

8. The two blocks remain stuck together as they are pulled to the right by a force F=200N. The coefficient of kinetic friction between block b and the table top is 0.800. a) Calculate the acceleration of the system b) calculate the force of friction between the two blocks. A) 5.5 m/s/s b) 173 N Exercise 115