Acceleration of 2.0kg Block: Solve Forces/Tension Problem

In summary, the 2.0 kg block is being pulled to the right with a tension force of 20 N while sitting on top of a 1.0 kg block that is tied to the wall with a rope. The coefficient of kinetic friction at both surfaces of the 2.0 kg block is 0.380. The net friction force on the lower surface is due to the normal reaction of 3 kg mass and is in the opposite direction of the applied force. The frictional force on the upper surface of the 2.0 kg block is due to the 1.0 kg mass and also opposes the applied force. The net friction force on the lower block is 8.832 N, resulting in an
  • #1
Dormin
1
0

Homework Statement


The 1.0 kg block in the figure is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is mu_k = 0.380.

knight_Figure_08_27.jpg


What is the acceleration of the 2.0 kg block?

Homework Equations


a = F/m
F_friction = mg * mu_k

The Attempt at a Solution


I found in a previous question that the tension of the rope holding the 1kg block, and thus the force of friction on the top of the 2kg block, was 3.72N (mg * mu_k = 9.8 * .38 = 3.72).

So the frictional force on the bottom of the 2kg block:

mg * mu_k = 2 * 9.8 * .38 = 7.448

Those two forces hold back the 20N force pulling to the right, so the total force acting on it to the right is:

20 - 3.72 - 7.448 = 8.832

So using a = F/m:

a = 8.832 / 2 = 4.416 m/s^2

However, 4.416 is incorrect. Any help you could give would be appreciated. Thanks!
 
Last edited:
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  • #2
The upper friction done by the 1-kg block is okay (3.72N), but I see a problem in the friction on the bottom, you should check what's the real mass affecting to that second friction.
 
  • #3
Hi Dormin, welcome to PF.
Net friction force on the lower surface is due to the normal reaction of 3 kg mass. It is in the opposite direction of 20 N. Frictional force on the upper surface of 2 kg block is due to 1 kg mass. It is also in the opposite direction of applied force.
Now find the net friction force on the lower block which opposes the applied force.
 

1. What is acceleration and how is it calculated?

Acceleration is the rate of change of velocity over time, or how quickly an object's speed is changing. It is calculated by dividing the change in velocity by the change in time.

2. How do you solve for forces in an acceleration problem?

To solve for forces in an acceleration problem, you need to use Newton's second law which states that force equals mass times acceleration. You can also use a free-body diagram to visualize the forces acting on the object and use equations of motion to solve for specific forces.

3. What is the tension force and how is it related to acceleration?

The tension force is a pulling force that is transmitted through a string, rope, or cable. In an acceleration problem, the tension force is often used to balance out other forces acting on the object in order to achieve a net acceleration of zero.

4. What information do you need to solve an acceleration problem?

To solve an acceleration problem, you need to know the mass of the object, the forces acting on the object, and the acceleration of the object. In some cases, you may also need to know the length of time the object experiences the acceleration.

5. Can you use calculus to solve for acceleration?

Yes, calculus can be used to solve for acceleration in certain situations, such as when the forces acting on the object are continuously changing. In these cases, you would use the derivative of the velocity function to find the acceleration.

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