Question

Notify Me Bookmark

Consider the Atwood machine in Fig. 1, where two blocks, one resting on top of the other. The blocks are tied to an ideal pulley (massless) through the rope and the rope can slip through the pulley without friction. The coefficients of static and kinetic frictions between the blocks are μ, and there is no friction between the block and the ground. Someone pulled the pulley with a force F. a. What will the maximum acceleration of the system be if the top block does not slip? ( 3 points) b. Now, assume that slipping does occur between the blocks. Draw the free-body diagrams of two blocks and the pulley w. (4 points) c. Express the acceleration of each block in terms of F, m1, m2, μ, and g when there is slipping. (Hint: pulley is massless, so the sum of the tensions in the rope equals to F ) (3 points)

Consider the Atwood machine in Fig. 1, where two blocks, one resting on top of the other. The blocks are tied to an ideal pulley (massless) through the rope and the rope can slip through the pulley without friction. The coefficients of static and kinetic frictions between the blocks are μ, and there is no friction between the block and the ground. Someone pulled the pulley with a force F. a. What will the maximum acceleration of the system be if the top block does not slip? ( 3 points) b. Now, assume that slipping does occur between the blocks. Draw the free-body diagrams of two blocks and the pulley w. (4 points) c. Express the acceleration of each block in terms of F, m1, m2, μ, and g when there is slipping. (Hint: pulley is massless, so the sum of the tensions in the rope equals to F ) (3 points)

Image text
  1. Consider the Atwood machine in Fig.1, where two blocks, one resting on top of the other. The blocks are tied to an ideal pulley (massless) through the rope and the rope can slip through the pulley without friction. The coefficients of static and kinetic frictions between the blocks are μ , and there is no friction between the block and the ground. Someone pulled the pulley with a force F . a. What will the maximum acceleration of the system be if the top block does not slip? ( 3 points) b. Now, assume that slipping does occur between the blocks. Draw the free-body diagrams of two blocks and the pulley w. (4 points) c. Express the acceleration of each block in terms of F , m 1 , m 2 , μ , and g when there is slipping. (Hint: pulley is massless, so the sum of the tensions in the rope equals to F ) (3 points)

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

Consider two blocks M1 on top of M2 on a level table. There is no friction between block M2 and the table, but there is friction between block M1 and block M2. Denote the coefficients of static and kinetic friction between the blocks as μs and μk, respectively. The applied force F is applied to block M1 at an angle θ below the horizontal. The blocks start from rest. First, we will consider the situation where F is small enough that the two blocks stick together. (a) Draw free-body diagrams for the two masses. Be sure to label all forces and the direction of the accelerations. Also be sure to define an appropriate coordinate system for each free-body diagram. (b) Write down the Newton's second law equations for each block and each dimension (x and y). (c) Write down an inequality relating the force of friction and the normal force. (d) Identify the two Newton's third law pairs - i. e. the pairs of forces between the two blocks that are equal and opposite. (e) Find the acceleration of the blocks as a function of F, θ, M1, M2, g, μs, and μk. (You don't have to use all of these, but you will use at most these. ) (f) Find a condition on F such that the blocks stick together. i. e. Write an inequality in the form F ≤ Fmax for the blocks to stick together where Fmax is in terms of θ, M1, M2, g, μs, and μk.
Solution
0 0

As shown in Figure 3(a), a wooden block B with mass mB = 2.4 kg on a rough inclined plane is connected to a massless spring ( k = 160 N/m ) by a massless cord passing over a pulley P of radius R = 0.25 m and mass Mp = 0.60 kg. The angle of the inclined plane is θ = 37∘ and the coefficients of static and kinetic frictions are μs = 0.35 and μk = 0.30 respectively. The frictional force at the axle of the pulley is negligible. The pulley can be regarded as a solid disk. (a) The system is at rest and in this case, block B is on the verge of sliding down. Figure 3(a) i. Indicate (with labeled arrows) the forces acting on the pulley and the block. ii. Calculate the tension in the string and the extension of the spring. (You can assume that the tensions in the cord on either side of the pulley P are the same for this part.) (b) As shown in Figure 3(b), another wooden block A of mass mA = 1.2 kg made of the same material as block B is released from rest. It slides down a distance l down the rough inclined plane and collides with block B. The two blocks stick together and move down the incline with a common velocity v = 0.80 m/s immediately after collision and the pulley rotates. The cord does not stretch and does not slip on the pulley. Figure 3(b) i. Determine the distance l. ii. Determine the acceleration of the two blocks at the moment they move down together and the pulley starts to rotate. iii. Determine how much further down the slope the two blocks move together after they collide before the two blocks come to a momentary rest.
Solution
0 0

As shown in the figure, a block of mass m is at rest on a ramp inclined 30∘ to the horizontal, and another block of mass 2 3 m at rest on a ramp inclined 60∘. Two blocks are connected by a light, inextensible cord, and the cord passes on a light, frictionless pulley. The other end of the block of mass m is connected to an spring with a force constant k. The spring is neither compressed nor extended. (a) What is the maximum distance the blocks will move when the inclines are frictionless? Express the answer in terms of m, k, and the gravitational acceleration g. (b) Repeat (a) when the coefficients of kinetic friction are 1/3 for both blocks. (c) What is the change in the internal energy of the system composed of the blocks, the inclines, and the spring?
Solution
0 0