Question

Notify Me Bookmark

A small block of mass m rests on the rough, sloping side of a triangular block of block of mass M which itself rests on a horizontal frictionless table (see the figure). The rough incline surface has a coefficient of static friction μs. A) Suppose that you apply a horizontal force F to push the triangular block (see the figure). Explain what will happen to the small block if the applied force F is relatively small. You gradually increase force F, and explain what will eventually happen to the small block as the force is sufficiently large. B) Draw a free body diagram for each of the blocks m and M. What is the direction of acceleration of these two blocks when they stick and move together? How many forces act on each of the blocks m and M? How many Newton's 3rd law force pairs are there in these two free body diagrams? Set up a coordinate system fixed to the table. Is the block M an inertial frame? C) Determine the minimum horizontal force F such that the small block will start moving up the incline. Draw coordinate systems, and write down intermediate steps with equations.

A small block of mass m rests on the rough, sloping side of a triangular block of block of mass M which itself rests on a horizontal frictionless table (see the figure). The rough incline surface has a coefficient of static friction μs. A) Suppose that you apply a horizontal force F to push the triangular block (see the figure). Explain what will happen to the small block if the applied force F is relatively small. You gradually increase force F, and explain what will eventually happen to the small block as the force is sufficiently large. B) Draw a free body diagram for each of the blocks m and M. What is the direction of acceleration of these two blocks when they stick and move together? How many forces act on each of the blocks m and M? How many Newton's 3rd law force pairs are there in these two free body diagrams? Set up a coordinate system fixed to the table. Is the block M an inertial frame? C) Determine the minimum horizontal force F such that the small block will start moving up the incline. Draw coordinate systems, and write down intermediate steps with equations.

Image text
A small block of mass m rests on the rough, sloping side of a triangular block of block of mass M which itself rests on a horizontal frictionless table (see the figure). The rough incline surface has a coefficient of static friction μ s . A) Suppose that you apply a horizontal force F to push the triangular block (see the figure). Explain what will happen to the small block if the applied force F is relatively small. You gradually increase force F, and explain what will eventually happen to the small block as the force is sufficiently large. B) Draw a free body diagram for each of the blocks m and M . What is the direction of acceleration of these two blocks when they stick and move together? How many forces act on each of the blocks m and M? How many Newton's 3 rd law force pairs are there in these two free body diagrams? Set up a coordinate system fixed to the table. Is the block M an inertial frame? C) Determine the minimum horizontal force F such that the small block will start moving up the incline. Draw coordinate systems, and write down intermediate steps with equations.

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

A block of mass m sits on top of a slab of mass 4 m. The slab rests on a frictionless floor. The coefficient of static friction between the slab and the block is 0.60 whereas the coefficient of kinetic friction is 0.40 . The block is now pulled by a horizontal force of magnitude F to the left. (a) It is observed that the blocks move together as a system. In this case, is the friction between the contact surfaces of the block and the slab static friction or kinetic friction? Justify. (b) If m = 10 kg, what is the maximum value of the applied horizontal force, F for which the slab and the block move together as a system? (c) If the applied horizontal force is increased beyond the value you determined in part (b), describe what would be the change, if any, in the motion of the block and slab. Explain. (d) For F = 100 N, what would be the accelerations of the slab and the block individually if you expect them to be different?
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