What is the magnitude of the frictional force on m1?

[sonutulsiani]

Homework Statement

If m1 = 4.0kg, μs = 0.40, m2 = 2.0kg, θ = 30°, what is the magnitude of the frictional force on m1? Give your answer in Newtons, to one decimal place. Use g = 9.81 m/s2.

http://bcs.whfreeman.com/WebPub/Physics/tiplerphysics6e_bridge/question_bank_images/fig5-62.png?2908

Homework Equations

Fs=μs Fn

The Attempt at a Solution

I am getting the answer as 0. Is it right?

 

[physicsface]

Please show how you obtained your answer.

You can find the force on m₂ using its mass and gravity. The net force on m₂ will be the same as the net force on m₁. Use the information you're given to find the gravitational force on m₁. Once you've got that, find the disparity between the force on m₁ and the force on m₂.

 

[tomcue]

The answer of 0 is not correct. To find the magnitude of the frictional force on m1, we can use the equation Fs=μsFn, where μs is the coefficient of static friction and Fn is the normal force. The normal force can be found by using Newton's second law, which states that the sum of the forces on an object equals its mass times its acceleration (ΣF=ma). In this case, the only forces acting on m1 are its weight (mg) and the normal force from m2 (N). We can set up the following equations:

ΣF=ma
mg+N=ma

We can also use trigonometry to find the value of N, since we know the angle θ and the weight of m2 (m2g). Using the equation N=m2gcosθ, we can substitute this into our second equation to get:

mg+m2gcosθ=ma

We can then solve for the normal force N, which will also be equal to the frictional force Fs.

N=ma-mg-m2gcosθ

Now, we can plug in the given values to find the normal force and the frictional force:

N=(4.0kg)(9.81 m/s2)- (4.0kg)(9.81 m/s2)- (2.0kg)(9.81 m/s2)cos(30°) = 19.62 N

Therefore, the magnitude of the frictional force on m1 is 19.62 N. It is important to note that this is the maximum possible static frictional force, as it is equal to μsFn. If the force applied to m1 exceeds this value, the object will start to move and the frictional force will decrease.