Connected Objects Problem Set
Follow the Problem Set Instructions & Rubric to complete and submit the following questions:
1. An Atwood machine consists of masses of 3.8 kg and 4.2 kg. What is the acceleration of the masses? What is the tension in the rope? [Answer: 0.49 \( m/s^2 \) [up], 39 N]
2. The smaller mass on an Atwood machine is 5.2 kg. If the masses accelerate at \( 4.6 m/s^2 \), what is the mass of the second object? What is the tension in the rope? [Answer: 14 kg, 72 N]
3. The smaller mass on an Atwood machine is 45 kg. If the tension in the rope is 512 N, what is the mass of the second object? What is the acceleration of the objects? [Answer: 1.6 \( m/s^2 \), 61 kg]
4. A 3.0 kg counterweight is connected to a 4.5 kg window that freely slides vertically in its frame. How much force must you exert to start the window opening with an acceleration of \( 0.25 m/s^2 \)? [Answer: 18 N [up]]
5. Two gymnasts of identical 37 kg mass dangle from opposite sides of a rope that passes over a frictionless, weightless pulley. If one of the gymnasts starts to pull herself up the rope with an acceleration of \( 1.0 m/s^2 \), what happens to her? What happens to the other gymnast?
6. a) Show that if the sliding block is now on an inclined plane set at an angle, \( \theta \), the acceleration is given by
\( a=( \frac{m_2-m_1sin \theta- \mu m_1 cos \theta }{m_1+m_2} )g \)
b) Show that this reduces the equation derived earlier on a flat plane.
c) Use this equation to determine the acceleration of a hanging mass of 15 kg, a inclined mass of 8.0 kg, an angle of \( 25^o \) and a coefficient of friction of 0.050. [Answer: 4.8\( m/s^2 \) [down]]