system C pulley / air cart me hanging P mass mn system Figure 1. An air-track ca

Question

system C pulley / air cart me hanging P mass mn system Figure 1. An air-track cart and a hanging mass are connected by a light string passing over the pulley of a rotary motion sensor. Use what you have learned during the last few weeks and the handout for this week's activity to answer questions 1-4 below. You may work with other students to develop a problem-solving strategy, but describe your reasoning in your own words. Defining the System: 1. Draw a clearly labeled free-body diagrams for System C and System H. (2 pts) 2. Write out the Newton's 2d Law equation for each mass. Explain your reasoning. (2 pts) 3. If the pulley friction is sufficiently low, the tension in the string is the same for both objects. Solve the two Newton's 2nd Law equations for Fnution and create a single equation that relates the acceleration of the system, a, to the hanging mass, m, the total mass of the system, Mm+ma, and the incline angle, 0. (2 pts) Evaluate your overall equation. In each case, explain your reasoning. 4. a. What does the model predict for the relationship between a and m? (2 pts) b. What does the model predict for the relationship between a and M? (2 pts)

Explanation / Answer

For air cart,

Ftension - mc*g*sin() = mca ..............(1)

For hanging mass,

mhg - Ftension = mha .................(2)

(1)+(2) gives,

mhg - mc*g*sin() = mca + mha

=> mhg - mc*g*sin() = (mc + mh)a

=> mhg - mc*g*sin() = Ma ..............(3)

relation between 'a' and 'mh' : mh = (Ma/g) + mc*sin()

relation between 'a' and 'M' : a = (1/M)[mhg - mc*g*sin()]

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