Applications of Newtons Laws (friction)

[sucksatphysic]

Homework Statement

At the airport, you pull a 18-kg suitcase across the floor with a strap that is at an angle of 45 deg above the horizontal. Find

a) Normal force and

b) the tension in the strap, given that the suitcase moves with constant speed and that the coefficient of kinetic friction b/w the suitcase and the floor is 0.38.

Homework Equations

N + mg +fk+ f = ma

I'm not sure if this equation is correct because they don't give you an initial force...

Y comp: N-mg + Fsin(theta) = 0

The Attempt at a Solution

I just need to know if my equations are right because the don't give an initial force. help?

 

[Delphi51]

I like "Y comp: N-mg + Fsin(theta) = 0".
I think you'll have to write a force equation like that for the horizontal part, too.
Likely you'll have two unknowns N and F, which you can solve for when you have the two equations.

 

[tomcue]

I can confirm that your equations are correct. The equation N + mg + fk + f = ma is a valid representation of Newton's Second Law, where N represents the normal force, mg represents the weight of the suitcase, and fk and f represent the kinetic friction force and the applied force, respectively. Since the suitcase is moving at a constant speed, the acceleration is zero and the equation can be simplified to N + mg + fk = 0.

For part a, to find the normal force, we can use the Y component equation N - mg cos(theta) = 0, where theta is the angle of 45 degrees. Solving for N, we get N = mg cos(theta). Plugging in the values of m (18 kg), g (9.8 m/s^2), and cos(theta) (cos(45) = 0.707), we get N = 124.92 N.

For part b, to find the tension in the strap, we can use the X component equation N - mg sin(theta) - fk = 0. Solving for fk, we get fk = N - mg sin(theta). Again, plugging in the values, we get fk = 124.92 N - (18 kg)(9.8 m/s^2)(sin(45) = 0.707) = 49.97 N. This is the tension in the strap required to maintain a constant speed.

In conclusion, Newton's Laws, specifically the equations for forces and components, can be applied to solve for the normal force and tension in the strap in this scenario. The coefficient of kinetic friction also plays a crucial role in determining the required tension in the strap. This application of Newton's Laws in understanding and predicting the motion of objects is a fundamental aspect of physics and has many practical applications in various fields.