PHYA11H3 Lecture 14: [PHYA11][Lec 14-[Chap. 5_ Forces and Motion, Short Catalogue of Forces,Identification of Forces, What Do Forces Do_, Inertial Reference Frames, Free Body Diagram ]

<p>A Simple Atwood Machine consists of two masses m1 and m1 that are connected by a string wound over a pulley, as seen in the figure below. m2 is larger than m1.<br />On a piece of paper, draw two free body diagrams; one for each of the masses, showing all forces acting on each mass. Then answer the following questions.<br /><br /><br />(a) Based on your free body diagram, identify the forces acting on the mass m1. Select all that apply.<br />(m1+m2)a<br />m1g<br />FN<br />m1a<br />(m1+m2)g<br />m2a<br />f<br />m2g<br />T<br /><br /><br /><br />(b) Using the direction rosette indicate the direction for each of the forces acting on m1 that you identified in part (a). If any of the forces listed below is not applicable, enter NA.<br />m1a= <br />m2a= <br />m1g= <br />m2g= <br />(m1+m2)a= <br />(m1+m2)g= <br />f= <br />T= <br />FN= <br /><br />(c) Based on your free body diagram, identify the forces acting on the mass m2. Select all that apply.<br />T<br />(m1+m2)g<br />m2g<br />m1g<br />(m1+m2)a<br />m1a<br />m2a<br />f<br />FN<br /><br /><br /><br />(d) Using the direction rosette indicate the direction for each of the forces acting on m2 that you identified in part (c). If any of the forces listed below is not applicable, enter NA.<br />m1a= <br />m2a= <br />m1g= <br />m2g= <br />(m1+m2)a= <br />(m1+m2)g= <br />f= <br />T= <br />FN= <br /><br />(e) Write Newton's Second Law equation (in the form Fnet = ma) for m1 in the y-direction.<br />Use the first answer box for the left hand side (LHS) of the equation and the second answer box for the right hand side (RHS) of the equation.<br />It is important to use the correct signs for each of the forces. Motion in the upward direction is positive and motion in the downward direction is negative. (Use m1, g, a, and T as appropriate.)<br />LHS = <br />RHS = <br /><br />(f) Write Newton's Second Law equation (in the form Fnet = ma) for m2 in the y-direction.<br />Use the first answer box for the left hand side (LHS) of the equation and the second answer box for the right hand side (RHS) of the equation.<br />It is important to use the correct signs for each of the forces. Motion in the upward direction is positive and motion in the downward direction is negative.(Use m2, g, a, and T as appropriate.)<br />LHS = <br />RHS = <br /><br />(g) Use your answers from parts (e) and (f) to get an expression for the magnitude of the tension T. (Use m1, m2, and g as appropriate.)<br />magnitude of T = <br /><br />(h) Use your answers from parts (e), (f), and (g) to find the magnitude of a, the acceleration of the system. (Use m1, m2, and g as appropriate.)<br />magnitude of a = <br /><br />(i) In what direction will each mass accelerate.<br />For mass m1: <br />For mass m2: <br /><br />(j) Suppose m1 = 7 kg and m2 = 11 kg. What is the tension in the string? <br />T = <br /><br />(k) Suppose m1 = 7 kg and m2 = 11 kg. What is the value of the acceleration?<br />a = <br /><br />(l) Suppose that m2 starts from rest at a height of 5 m. Use the Kinematic Equations to determine how long it takes for m2 to hit the ground.</p>

I often find myself dragging my luggage through airports. Assumethat my luggage has a mass of 5.0 kg and that the coefficient ofkinetic friction k between the luggage and the airport floor is0.75 (recall that friction = coefficient of kinetic friction xnormal force). I drag the luggage at a constant speed of 3.0 m/s byapplying a force at an angle of 60o to the floor. Assume that Istart from rest and finish my walk at rest.

a. Why would it be difficult to calculate the total effort I expendin dragging my luggage using Newton's laws alone?

b. What is the total work done on the luggage? How does this allowus to get around the problem in part a)?

c. Draw a free-body diagram of all the forces acting on theluggage. Which forces do non-zero work on the luggage? Try tocalculate the work done by me, friction, and the force of gravityas I drag the luggage 100 m from the check-in desk to the gateacross a horizontal floor. Use the fact that you start from restand end at rest. If you get stuck in the math, describe the generalway you would approach this problem: which work would you calculatefirst, which last?

A beam resting on two pivots has a length of L = 6.00 m and mass M= 92.0 kg. The pivot under the left end exerts a normal force n1 onthe beam, and the second pivot placed a distance script i = 4.00 mfrom the left end exerts a normal force n2. A woman of mass m =50.0 kg steps onto the left end of the beam and begins walking tothe right as in the figure below. The goal is to find the woman'sposition when the beam begins to tip.
(a) Sketch a free-body diagram, labeling the gravitational andnormal forces acting on the beam and placing the woman x meters tothe right of the first pivot, which is the origin. (Do this onpaper. Your instructor may ask you to turn in this work.)

(b) Where is the woman when the normal force n1 is thegreatest?
1

(c) What is n1 when the beam is about to tip?
2. N

(d) Use the force equation of equilibrium to find the value of n2when the beam is about to tip.
3. N

(e) Using the result of part (c) and the torque equilibriumequation, with torques computed around the second pivot point, findthe woman's position when the beam is about to tip.
4. m

(f) Check the answer to part (e) by computing torques around thefirst pivot point.
5. m

Except for possible slight differences due to rounding, is theanswer the same?
6. Yes/No