2. A 6 kg mass and a 14 kg mass are suspended by a pulley with a radius of 18 cm and a mass of 4.5 kg. The cord has a negligible weight and causes the pulley to rotate without slipping. The pulley rotates without friction. The masses start from rest when they are 2.5 m apart. Treat the pulley as a uniform disk. Find: a. The speeds of the two masses when they meet at the same height. b. The angular velocity of the pulley at that time; c. The acceleration of the two masses. d. The Tension of the strings. e. The angular acceleration of the pulley. Solve this problem using Energy method.
Added by Brian H.
Close
Step 1
The potential energy of the masses can be given by the equation: \[PE = mgh\] where m is the mass, g is the acceleration due to gravity, and h is the height. Show more…
Show all steps
Your feedback will help us improve your experience
Manish Jain and 55 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in the figure. The pulley has mass mp and radius R and turns on frictionless bearings. The mass m1 slides on a horizontal, frictionless surface. Mass m2 is released when the blocks are at rest. The moment of inertia of the pulley is I = MR^2/2. (a) Draw the FBD for each of the three objects, m1, m2, and mp. (b) Apply Fnet = ma for each of the two blocks. (c) Can both parts of the string have the same tension? Explain. What are the torques of the tension forces on the left and right side of the pulley about the axis of the pulley in terms of T1 and T2? Hint: Draw the moment arm in each case. What is the net torque? Apply τnet = Iα for the pulley. (d) How is the acceleration of the blocks related to the angular acceleration of the pulley? (e) Combine the three equations from part (b) and (c) to find the acceleration of m1 and m2 and the angular acceleration of the pulley.
Manish J.
An Atwood machine consists of two masses, one 5.5 kg on the left and high and the other 3.5 kg on the right and lower, which hang together by a rope that passes through a pulley, the fixed axis of which is held from the ceiling by another rope. The pulley is disk-shaped, solid, with a mass of 2.5 kg and a radius of 7.5 cm. (Inertia = ½ MR²). So that the rope does not come off, it passes through a channel and its effective radius at the center of the pulley is 7.0 cm. The rope does not slide in its channel, the friction between the rope and the pulley is static. Other frictions on the pulley shaft are very small. The mass of the rope is negligible. a) Make a drawing of the system clearly indicating the forces involved in the movement. The unknown forces indicate them in letters. Notice that the tension in the rope is not the same on both sides (why?) b) Make the free-body diagram of each body (there are three bodies: the two masses and the pulley) and establish the equations of motion for each. c) Write the relationship between the acceleration of the blocks and the angular acceleration of the pulley. d) How many unknowns are there? How many equations? From the equations of the blocks, solve for the tensions. Plug in the equation for the pulley and finally calculate the angular acceleration of the pulley. e) Calculate the values of the tensions.
Adriano C.
An Atwood machine consists of two masses, one 5.5 kg on the left and high and the other 3.5 kg on the right and lower, which hang together by a rope that passes through a pulley, the fixed axis of which is held from the ceiling by another rope. The pulley is disk-shaped, solid, with a mass of 2.5 kg and a radius of 7.5 cm. (I = ½ MR²). So that the rope does not come off, it passes through a channel and its effective radius at the center of the pulley is 7.0 cm. The rope does not slide in its channel, the friction between the rope and the pulley is static. Other frictions on the pulley shaft are very small. The mass of the rope is negligible. a) Make a drawing of the system clearly indicating the forces involved in the movement. The unknown forces indicate them in letters. Notice that the tension in the rope is not the same on both sides (why?) b) Make the free-body diagram of each body (there are three bodies: the two masses and the pulley) and establish the equations of motion for each. c) Write the relationship between the acceleration of the blocks and the angular acceleration of the pulley. d) How many unknowns are there? How many equations? From the equations of the blocks, solve for the tensions. Plug in the equation for the pulley and finally calculate the angular acceleration of the pulley. e) Calculate the values of the tensions.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD