# Tension with horizontal kinetic friction

• AnkhUNC
In summary, tension with horizontal kinetic friction is a force that acts on an object as it moves horizontally across a surface with friction. It is affected by factors such as the object's mass, coefficient of friction, and acceleration. The formula for calculating tension is T = μk * m * g, and an increase in the coefficient of friction will result in an increase in tension. However, tension can be reduced by decreasing the coefficient of friction, reducing the force or acceleration, or using lubricants or different surface materials.
AnkhUNC
[SOLVED] Tension with horizontal kinetic friction

## Homework Statement

In Figure, block 1 of mass m1 = 1.8 kg and block 2 of mass m2 = 1.3 kg are connected by a string of negligible mass. Block 2 is pushed by force of magnitude 20 N and angle θ = 39°. The coefficient of kinetic friction between each block and the horizontal surface is 0.22. What is the tension in the string?

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c06/fig06_61new.gif

## The Attempt at a Solution

This is what I end up with but its wrong:
20*cos(39)-20*sin(39)*0.22-
1.3*g*0.22-T=1.3*a

and
T-1.8*g*0.22=1.8*a

Solving for T =

a=T/1.8-g*0.22

20*cos(39)-20*sin(39)*0.22-
1.3*g*0.22-T=1.3*(T/1.8-g*0.22)

(20*cos(39)-20*sin(39)*0.22-
1.3*g*0.22+1.3*g*0.22)*1.3/(1/1.8+1)=T

10.7 N

= T

I have read your post and I believe I can provide some assistance. First, I would like to clarify the problem statement. Are the blocks on a horizontal surface or are they on an inclined plane? Also, is the string connecting the blocks horizontal or at an angle? This information will be necessary in order to accurately solve the problem.

Assuming that the blocks are on a horizontal surface and the string is also horizontal, the first step would be to draw a free body diagram for each block. For block 1, the forces acting on it would be its weight (mg) and the tension in the string (T). For block 2, the forces would be its weight (mg), the applied force (20 N) at an angle of 39°, and the tension in the string (T).

Next, we can write out the equations of motion for each block. For block 1, the equation would be ΣF=ma, where ΣF is the sum of all the forces acting on the block. This would give us:

T-m1g=0

For block 2, the equation would be ΣF=ma, where ΣF is the sum of all the forces acting on the block. This would give us:

T-m2g-20cos(39)=m2a

We can also use the fact that the coefficient of kinetic friction is given as 0.22 to write out an equation for the frictional force acting on each block. This would be:

μkN=m1g and μkN=m2g

Where N is the normal force acting on each block.

Now, we can substitute the value of N into the equations for each block to get:

T-0.22m1g=0 and T-0.22m2g-20cos(39)=m2a

We can then solve these equations simultaneously to get the value of T, which would be the tension in the string. I hope this helps. Let me know if you have any further questions or need clarification on any of the steps. Good luck with your problem solving!

= T

The tension in the string is 10.7 N.
Based on the given information, it seems like you have correctly set up the equations for the tension in the string. However, there may be a mistake in your calculations as the final answer of 10.7 N does not seem to match the given values. I would recommend double-checking your calculations and equations to ensure accuracy. Additionally, it may be helpful to label your equations and variables clearly to avoid any confusion. Overall, your approach to the problem seems correct, but it is important to carefully check your work to arrive at the correct answer.

## What is tension with horizontal kinetic friction?

Tension with horizontal kinetic friction is a concept in physics that describes the force exerted on an object as it moves horizontally across a surface with friction. This force is caused by the interaction between the object and the surface, and it acts in the opposite direction to the direction of motion.

## What factors affect the tension with horizontal kinetic friction?

The tension with horizontal kinetic friction depends on several factors, including the mass of the object, the coefficient of friction between the object and the surface, and the acceleration or deceleration of the object. Additionally, the angle at which the object is moving and the surface roughness can also affect the tension.

## How is tension with horizontal kinetic friction calculated?

The tension with horizontal kinetic friction can be calculated using the formula T = μk * m * g, where μk is the coefficient of friction, m is the mass of the object, and g is the acceleration due to gravity. This formula assumes that the object is moving at a constant speed and that the surface is horizontal.

## What happens if the coefficient of friction is increased?

If the coefficient of friction is increased, the tension with horizontal kinetic friction will also increase. This means that more force will be required to move the object across the surface, and the object may move at a slower speed or come to a complete stop.

## Can tension with horizontal kinetic friction be reduced?

Yes, tension with horizontal kinetic friction can be reduced by either decreasing the coefficient of friction or by reducing the force or acceleration acting on the object. In some cases, adding a lubricant or changing the surface material can also decrease the friction and, therefore, the tension.

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