10. 11. 12. Homework 4 How many forces are required for an interaction? To produce a net force on a system, must there he an externally applied net force? Earth pulls down on you with a gravitational force that you call your weight. Do you pull up on Earth with the same amount of force? How does a helicopter get its lifting force? What happens to the magnitude of the normalvector on a block resting on an incline when the angle of the incline increases? How does the magnitude of the vertical component of velocity for a ball tossed at an upward angle change as the hall travels upward? How about the horizontal component of velocity when air resista nce is negligible? For each of the following interactions, identify action and reaction forces: (at A hammer hits a nail. {[1} Earth gravity pulls down on a book. {1:} A helicopter blade pushes air downward. Consider the two forces acting on the person who stands stillnamely, the downward pull of gravity and the upward sUpport ofthe floor. Are these forces equal and opposite? Do they form an action reaction pair? Win! or why not? .. .J Suppose thattwo carts. one twice as massive as the other, fly apart when the compressed spring that joins them is released. 'what is the acceleration of the heavier cart relative to that of the lighter cart as they start to move apart? If a Mack truck and Honda Civic have a head-on collision. upon which vehicle is the impact force greater? Which vehicle experiences the greater deceleration? Explain your answers. Consider a hall rol ling around in a circular path on the inner surface of a cone [see the gure below]. The weight of the hall is shown by the vector till. Iwithout friction, only one other force acts on the halla normal force. [a]- Draw in the vector for the normal force. {T he length of the vector depends on the next step, b.) [b] Using the parallelogram rule, show that the resultant of the two vectors is along the radial direction of the hall's circular path. (Yes, the normal is appreciably greater than the weightl} Suppose you roll a ball off a tabletop. Will the time to hit the oor depend on the speed of the hall? [Will a fast ball take a longer time to hit the floor?) Defend your answer. Lab 6 - Dynamics: F = ma Introduction: the source of acceleration forcel That is a fare es a more to accelerate Think about some examples of acceleration from everyday life. In each case, what is the force (or forces) that cause this acceleration? Is the Earth accelerating in its movement around the Sun? If so what force causes that acceleration? arce on some masses on a string. This the masses in the system : the mass of the car the masses that are placed on the car and the mass" (You could just as easily call it the "total mass') In summary, the weight of the masses on the string causes the "system mass" to accelerate." Purpose: To explore the relationship between acceleration, mass, and unbalanced force (also called net orce). and to verify Newton's Second Law. car plus additional masses Newton's Second Law all of the masses: weight: F = mg According to Newton's Second Law (F = Ma), the unbalanced force is his lab, we test this by taking some mass off the car and placing it on the hanger at the end of the string. Note that the "system mass" has not changed. What we are doing is distributing the "system mass" so that more of it is at the end of the string. This causes more force to be exerted on the string (why?). In the lab we will see if this results in more acceleration, as we expect it to. We can use the force and the acceleration to calculate the total mass in the system, which we can also determine by direct measurement. We hope they agree with each other! The details: The acceleration along the air track is given by the equation of motion d = zar where d is the distance between the photo sensors, and t is the time it takes for the car to travel between the sensors. Solving this equation for a, we get: unbalanced or net force that causes this acceleration is the weight of the hanging masses he string (other forces cancel out each other): where m is the total mass on the hanger plus the mass of the hanger and g is the acceleration due to gravity and is equal to 9.8 m/s?. his force is responsible for the acceleration of all of the mass in the system. We can call this ora mass the system mess , let these to the sum ofthe mass ofme hanger. the mass of the car to the hanger, the total mass stays the same. Thus, the "system mass" does not change.) masses (which is the same as the acceleration of the car): where F is the weight of the mass on the hanger, given above. "system mass", described aboy and a is the acceleration of the masses Things to Remember: centimeters (cm) or millimeters (mm). However, the calculations should use units of kilograms and meters. centimeters (cm) to meters (m), divide by 100 To convert from milimeters (mm) to meters (m), divide by 1000. To compare the measured value with the actual value: percent difference = [measured value - actual valuel x 100 (actual value) Air track operation: You may turn the air off when the air track is not needed (otherwise the room gets too noisy). Be the car along the track when there is no air in the air track. This will scratch the air track, making it less accurate. Procedure: Relevant video: https:/www.youtube.com/watch?v=OhhDooJW10Q elow is a procedure that was carried out leading to the table in the following table 1) Make sure air track is level 2) Measure the mass of the car on the triple beam balance. Measure the distance between the photo sensors. Record the data. 3) Start with no mass on the hanger and 40 g attached to the car Experiment to find the best position. It is important that the car be as close as possible to the first sensor. When moving the car along the air track, make sure the air is on. 5) When you're ready I begin to accelerate. 6) After the car has passe nsor, record the time displayed on the timer. 6) Take 5 g off of the car, and add 5 g to the hanger. Repeat steps 4-6 with these new masses () when you have filled out the data table, calculate the acceleration. Make a plot of represents these points. The points will not likely fall exactly in a line, but they should be fairly close. 8) For each trial, calculate the mass using m = =. In each case, the mass you calculate should a be equal to the "system mass . which is the total mass of the system (mass of the car plus the between the actual "system mass" and the measured "system mass" from the data table. Data, Part I: mass of car (measured with triple beam balance): 0.308 kg actual "system mass" (mass of car + mass of hanger + 40 g): 0.353 KC distance between sensors d: 0.50 m = m - 20 2.596 10 1.814 10 15 1.553 15 1.338 1.147 1.093 Discussions & Conclusions in your conclusion, discuss whether or not we achieved the goal set out in the "Purpose" change? How did the acceleration change? is miss mass to the hanger, how did the time What contributed to the percent difference? How did the equipment affect the results