A solid cylinder of mass m is placed over a plank of same mass as shown in figure. The plank is placed on smooth horizontal surface. There is sufficient friction between cylinder and plank to prevent slipping. If a force is applied at the centre of the cylinder then find the ratio of magnitude of acceleration of cylinder to magnitude of the acceleration of the plank.
Question
A solid cylinder of mass m is placed over a plank of same mass as shown in figure. The plank is placed on smooth horizontal surface. There is sufficient friction between cylinder and plank to prevent slipping. If a force is applied at the centre of the cylinder then find the ratio of magnitude of acceleration of cylinder to magnitude of the acceleration of the plank.
Solution
To solve this problem, we need to use the principles of Newton's second law of motion and the concept of friction.
Step 1: Identify the forces acting on the system The force F is applied to the cylinder, and there is friction between the cylinder and the plank. Since there is no slipping, the frictional force will cause the plank to move as well.
Step 2: Apply Newton's second law to the cylinder The net force acting on the cylinder is F - f (where f is the frictional force). According to Newton's second law, F - f = m*a_c (where a_c is the acceleration of the cylinder).
Step 3: Apply Newton's second law to the plank The only force acting on the plank is the frictional force f. So, f = m*a_p (where a_p is the acceleration of the plank).
Step 4: Solve the equations From step 2, we have f = F - ma_c. Substituting this into the equation from step 3, we get F - ma_c = m*a_p. Rearranging, we get a_c/a_p = (F/m - a_p) / a_p = F/m * 1/a_p - 1.
Step 5: Find the ratio of the accelerations The ratio of the accelerations a_c/a_p is equal to F/m * 1/a_p - 1. Since F, m, and a_p are all positive, the ratio a_c/a_p is greater than 1. This means that the cylinder accelerates faster than the plank.
Note: This solution assumes that the frictional force is sufficient to prevent the cylinder from slipping on the plank. If the frictional force is not sufficient, the cylinder will slip and the accelerations will be different.
Similar Questions
A string is wrapped around a uniform solid cylinder of radius r𝑟, as shown in (Figure 1). The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m𝑚.Figure1 of 1Part AFind the magnitude α𝛼 of the angular acceleration of the cylinder as the block descends.Express your answer in terms of the cylinder's radius r𝑟 and the magnitude of the free-fall acceleration g𝑔.View Available Hint(s)for Part AHint 1for Part A. How to approach the problemHint 2for Part A. Find the net force on the blockHint 3for Part A. Find the net torque on the pulleyHint 4for Part A. Relate linear and angular accelerationHint 5for Part A. Putting it togetherActivate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeα𝛼 =2(g+a)r
A plate of mass m is placed on a frictionless surface. The plate is connected to block of mass M through a string over a massless pulley. A cylinder of mass m is placed on the plate which rolls without slipping. Find the frictional force acting on the cylinder:
A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 5.00 m2. The height of the lower part of the container is 2.50 m and the neck contains a column of water 8.50 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container?
A disc of mass m and radius R is placed over a plank of mass m. There is sufficient friction between disc and plank to prevent slipping and there is no friction between plank and ground. A horizontal force F is applied at the centre of the disc, then
A massless string is wrapped around a solid cylinder of mass 0.400 kg and radius 0.100 m. The string is attached to the ceiling. The cylinder is released. As it falls, the string unwinds. What is the magnitude of the acceleration of the cylinder as it falls?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.