Blocks, Tension, Acceleration, Friction Problem

In summary: The tension in the string is the same in all places. Sum the forces on A and B, then consider the forces on C.
  • #1
trc214
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Homework Statement


Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop. There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest?



Homework Equations


f=ma
coefficient of static friction = Fmax/normal force



The Attempt at a Solution


At first I took found the weights of blocks A and B.

[w Block A = 8.00kg(9.8m/s^2)] = 78.4 N
[w Block B = 5.00(9.8m/s^2)] = 49 N

w of A+B = 78.4+49= 127.4 N

I calculated that the normal force of Blocks A+B = 127.4 N. Then since the weight of block C which is unknown would equal the tension in the rope, I figured I would use this information using the coefficient of friction to find the mass of block C.

So then I set 0.750 which was the coefficient of friction = to fmax/normal force.

0.750 = Fmax/127.4

I found the Fmax=36.75 N

Then I divided 36.75 N by g to get the mass of block C. I got the mass of block C to be 3.75 kg. Apparently this is incorrect and the correct answer is 9.75 kg.

Can anyone pease help me? Thank you very much.
 
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  • #2
trc214 said:

Homework Statement


Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop. There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest?



Homework Equations


f=ma
coefficient of static friction = Fmax/normal force



The Attempt at a Solution


At first I took found the weights of blocks A and B.

[w Block A = 8.00kg(9.8m/s^2)] = 78.4 N
[w Block B = 5.00(9.8m/s^2)] = 49 N

w of A+B = 78.4+49= 127.4 N

I calculated that the normal force of Blocks A+B = 127.4 N.
This is the normal force of the floor on Block A
Then since the weight of block C which is unknown would equal the tension in the rope, I figured I would use this information using the coefficient of friction to find the mass of block C.
It would only equal the rope tension if it was at rest or moving at constant velocity. Is it?
So then I set 0.750 which was the coefficient of friction = to fmax/normal force.

0.750 = Fmax/127.4

I found the Fmax=36.75 N
127.4 N is not the normal force of A on B
Then I divided 36.75 N by g to get the mass of block C. I got the mass of block C to be 3.75 kg. Apparently this is incorrect and the correct answer is 9.75 kg.

Can anyone pease help me? Thank you very much.
It may be late, but I don't get the book answer. Draw free body diagrams to identify the forces on each mass, and use Newton's laws. All blocks are accelearting at the same magnitude.
 

1. What is the difference between blocks, tension, acceleration, and friction?

Blocks, tension, acceleration, and friction are all related concepts in physics. Blocks refer to objects with mass that are used to demonstrate different principles in physics. Tension is a force that is transmitted through a rope, string, or cable when it is pulled on from opposite ends. Acceleration is the rate of change of an object's velocity over time. Friction is the force that resists the motion of an object when it comes into contact with another surface.

2. How do blocks, tension, acceleration, and friction affect each other in a problem?

In a problem involving blocks, tension, acceleration, and friction, these concepts are all interrelated and affect each other. The weight of the blocks and the tension in the ropes or cables can affect the acceleration of the system. Friction can also play a role in slowing down or stopping the motion of the blocks. The direction and magnitude of these forces must be taken into account in order to accurately solve the problem.

3. What are some common strategies for solving problems involving blocks, tension, acceleration, and friction?

One common strategy for solving these types of problems is to draw a free body diagram, which shows all the forces acting on the blocks. Another strategy is to break the system into smaller components and analyze each one separately. It is also important to accurately identify and label all the variables and equations involved in the problem before attempting to solve it.

4. What factors can affect the accuracy of solutions to problems involving blocks, tension, acceleration, and friction?

The accuracy of solutions to these types of problems can be affected by a number of factors. These include incorrect assumptions or simplifications, human error in calculations or measurements, and neglecting to account for all relevant forces or variables. It is important to carefully check all steps and assumptions when solving these problems in order to ensure accuracy.

5. How can understanding blocks, tension, acceleration, and friction be useful in real-world applications?

Understanding these concepts can be useful in a variety of real-world applications, such as engineering, construction, and transportation. For example, engineers use these principles to design structures and vehicles that can withstand different forces and motion. Understanding friction can also help in creating more efficient machines and reducing wear and tear on surfaces. Overall, a strong understanding of these concepts can be helpful in solving problems and making informed decisions in many different fields.

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