Ansrvenmlsbetweenredlaendnadls Given the example below (Chapter 7 Motion in a Circle. Knight Text) Wigwam: A 209 steel weight is placed on the edge of a 30cm diameter plastic disk- The coefcient of static friction between the steel weight and plastic disk is 0.4. At what angular velocity, or will the weight slide off the disk? Your solution should include "known'. a pictorial representation. a physical representation and a free-body diagram. Hint: Apply Newton's second law using v = rm, instead of v, as in the example below. Use the attached Dmamic Worksheet uamurt 3.6 Turning'recornerl What is the maximum speed with which a 1500 kg car can make a left turn around a curve of radius 50 m on a level mob-united} road without sliding? uoost Although the car turns only a quarter of a circle. we can model the car as a particle in uniform circular mien as it goes around the rum. Assume that rolling friction is negligible. visunttzc Figure 7.16 shows the pictorial and physical repre- sentations. The car moves along a circular are at constant speed for the quarter-circle necessary to complete the turn. The motion before and after the turn is not relevant to the problem. The more interesting issue is how a car turns a corner. \"that force or forces can we identify that cause the direction of the velocity vector to change? Imagine you are driving a car on a completely frictionless road. such as a very icy road. You would not be able to turn a corner. Turning the steering wheel would be of no use: the car would slide straight ahead. in accordance with both Newton's rst law and the experience of anyone who has ever driven on ice! So it must be friction that somehow allows the car to tum. The force-identication section of Figure 7.16 shows the top view of a tire as it turns a corner. If the road surface were fric- tionless. the tire would slide straight ahead. The force that pre- vents an object from sliding across a surface is static friction. Static friction f; pushes sideways on the tire. toward the center of the circle. How do we know the direction is sideways? If I: had a component either parallel to F or opposite to F, it would cause the car to speed up or slow down. Because the car changes direction hut not speed, static friction must be perpen- dicular to 3. Thus I; causes the Centripelal acceleration of circu- lar motion around the curve. With this in mind. the free-body diagram. drawn from behind the car. shows the static friction force pointing toward the center of the circle. sows Because the static friction force has a maximum value. there will be a maximum speed with which a car can turn with; out sliding. The maximum speed is reached when the static fric- tion force reaches its maximum ,\" - pun. If the car enters the curve at a speed higher than the maximum. static friction will not be large enough to provide the necessary centripetal acceleration and the car will slide. The static friction force points in the positive rdirection. so its radial component is simply the magnitude of the vector: (1;), = f... Newton's second law in the rtz-coordinate system is Econ? 2Fi-nw=0 Pictorial representation Physical representation Known Top view m =1500 kg of tire r = 50 m A = 1.0 Find Rear view max Top view of car of car FIGURE 7.16 Pictorial and physical representations of a car turning a corner. The only difference from Example 7.5 is that the tension force where we used n = w from the z-equation. At that point, toward the center has been replaced by a static friction force toward the center. From the radial equation, the speed is ris max Vmax VArg m = V (1.00) (50 m) (9.80 m/s?) = 22.1 m/s The speed will be a maximum when f, reaches its maximum where we found u, in Table 5.1. value ASSESS 22.1 m/s = 45 mph, a reasonable answer for how fast a car can take an unbanked curve. Notice that the car's mass can- f, = fomax = un = u,w = u,mg celed out and that the final equation for Vmax is quite simple. This is another example of why it pays to work algebraically until the very end.Given the example above (Chapter 7 Motion in a Circle, Knight Text) solve the following problem: A 20g steel weight is placed on the edge of a 30cm diameter plastic disk. The coefficient of static friction between the steel weight and plastic disk is 0.4. At what angular velocity, . will the weight slide off the disk? Your solution should include "known", a pictorial representation, a physical representation and a free-body diagram. Hint: Apply Newton's second law using v = ro, instead of v, as in the example. 1) Pictorial Representation a. sketch showing important points in the motion b. coordinate system c. symbols for knowns and unknowns Known: Find:()max 2) Physical Representation a. motion diagram b. force identification c. free-body diagram 3) Mathematical Representation a. start with Newton's first or second law b. include other information as needed c. solve! 2nd law for r-axis 2nd law for z axis