Assorted Short Newton's Law Problems - Practice Setting Up

For each of the following figures:

• Draw a ``free body diagram'' for each mass shown, that is, draw in and label all real forces acting on it;
• Apply Newton's Second Law in appropriate coordinates to each mass shown. In two of your three choices, do not proceed further; (5 points each for three.)
• Pick one figure and solve for the acceleration(s) of each mass shown and evaluate all unknown forces (such as a normal force or the tension in a string) in terms of the given quantities. (5 points for the one.)

Don't forget that the acceleration is a vector and must be given as a magnitude and a direction (for example, ``along the plane to the right'' is ok) or in vector components. (5 points each + 5 points for finding unknowns for one of them.)

1. $\theta = 36.87^\circ$, $m_1 = 10$ kg, $m_2 = 20$ kg, $\mu_k = 0.1$

   

   
   
   
   

2. $m_1 = m_2 = 8$ kg.

   

   
   
   
   

3. $r = 2.0$ m, $\theta = 45\circ$, $m = 5$ kg, $\vert\vec{v}\vert = 10$ m/sec.

   

4. Given: $\theta$, $m_1$, $m_2$, $\mu_k$ and $v_0 \ne 0$ to the right (the objects are already moving, so only kinetic friction applies regardless of their masses).

   

   
   
   
   

5. Given: $\theta$, $m_1$, $m_2$.

   

   
   

6. This is a block whirled on the end of a string sitting on a rough table. Gravity is into the page. Given: $R$, $m$, $v$, $\mu_k$, $\theta$.

   

   
   
   
   

7. A rope at an angle $\theta$ with the horizontal is pulled with a force F. It pulls, in turn, two blocks, the bottom with mass $M$ and the top with mass $m$. The coefficients of friction are $\mu_s$ between the top and bottom block (assume that they do not slide for the given force F) and $\mu_k$ between the bottom block and the table. Remember to show (and possibly evaluate) all forces acting on both blocks, including internal forces between the blocks.