# Webct3 - pulling 1 Two people pull a box of mass m = 10 kg with forces F1 and F2 which make angles f1 = 30 and f2 = 45 with the direction of motion

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pulling 1. Two people pull a box of mass m = 10 kg with forces F 1 and F 2 , which make angles f 1 = 30° and f 2 = 45° with the direction of motion. The acceleration of the box is a = 5 m/s 2 . Find the magnitude of F 1 . Applying Newton’s second law in the horizontal direction we get : F 1 cos30 ° + F 2 cos45 ° = ma Applying Newton’s second law in the vertical direction we get : F 1 Sin30 ° = F 2 Sin45 ° ( in this direction, a = 0 m/s 2 ) Thus we have two equations and two variables F 1 and F 2 . Solving these equations we get

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F 1 = 36.7 N F 2 = 26 N 2. Find the magnitude of F 2 . See feedback for part one.
Boxes with strings (1) 1. Three boxes labeled A, B and C with masses m , m and M ( M > m ), respectively, are attached with ideal massless strings as shown in the figure below. The string goes through an ideal pulley. Neglect friction and air resistance. Let a A , a B and a C be the magnitude of the accelerations of boxes A, B and C, respectively. Which of the following relations is true? a. a A < a B = a C b. a A = a B < a C c. a A = a B > a C d. a A < a B < a C *e. a A = a B = a C Unless the strings stretch or shrink, all three boxes must move together and thus have the same acceleration. 2. The acceleration of the hanging box is: *a. Smaller than g (9.81 m/s 2 ). b. Equal to g (9.81 m/s 2 ). c. Larger than g (9.81 m/s 2 ). A detailed free-body diagram is not needed here. We just need to consider: 1. What is the mass of the whole system? M +2 m

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2. What is the net force on the system? Mg (the only force that pulls on the system is the weight of block C, and there is no friction) Thus, the magnitude of the acceleration of the system will be 2 Mg ag Mm = < + . You can also think of a more extreme case. What do you expect to happen if instead of two boxes on the table, there were 100 of them (ie, increase the mass)? Or if m was very large? Or if m was zero? 3. Let F A , F B and F C be the magnitude of the net force on boxes A, B and C, respectively. Which of the following relations is true? a. F A < F B = F C *b. F A = F B < F C c. F A = F B > F C d. F A < F B < F C e. F A = F B = F C The acceleration of the three boxes are equal. For each box, the net force is equal to its mass times its acceleration. Since M > m , the force on box C is the highest and that of boxes A and B are equal. 4. Let T AB be the tension on the rope between boxes A and B and let T BC be the tension on the rope between boxes B and C. Which of the following is true? *a. T AB < T BC b. T AB = T BC c. T AB > T BC Intuitively: the string between A and B has to pull on the mass of block A only, whereas the string between B and C has to pull on a larger mass (2 m ). So T AB < T BC More detailed approach: Block A T AB Block B T BC T AB F net, on A F net, on B
The net force on both block must be the same (see part 3). Thus, by looking at the free- body diagram of block B, it is clear that we need T AB < T BC .

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elevator 1. A person of mass m = 75 kg stands on a bathroom scale inside an elevator. For the
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## This homework help was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Spring '08 term at Iowa State.

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Webct3 - pulling 1 Two people pull a box of mass m = 10 kg with forces F1 and F2 which make angles f1 = 30 and f2 = 45 with the direction of motion

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