Calculate Frictional Forces Needed for 6.5kg Shopping Cart on 13° Incline

[wind522]

I have a question..

A shopper pushes a 6.5kg shopping cart up a 13 degree incline, heading east. Find the magnitude of the horizontal force, F, needed to give the cart an acceleration of 1.61 m/s2 (seconds squared).

This is what I have done.
sigmaFx= F(what I'm trying to find) - Fg,x - Ff
MAnet = F - mgsin(theta) - u(mieu)Fn
F = MAnet + mgsin(theta) + uFn
F = (6.5kg)(1.61m/s2) + (6.5kg)(9.81m/s2)sin13 +u(63.13070718N)
And here's where I'm stuck because there's two variables. Does anyone know what I'm doing wrong?

The answer should be in Newtons

 

[Doc Al]

Are you supposed to be including friction? If so, you'll need the coefficient of friction.

Also, note that the applied force is horizontal, thus if you are finding components parallel to the incline you must take that into account.

 

[baba89]

(N).

I would first clarify the given information and make sure all units are consistent. The mass is given in kilograms, the acceleration is given in meters per second squared, and the angle is given in degrees. It would be helpful to convert the angle to radians since the trigonometric functions used in the equation require radians as input.

Next, I would use the equation for Newton's Second Law, F = ma, to find the net force acting on the shopping cart. The net force is equal to the sum of all forces acting on the cart, which in this case includes the applied force (F), the force of gravity (Fg), and the force of friction (Ff).

To find the force of gravity, we can use the equation Fg = mg, where m is the mass and g is the acceleration due to gravity (9.81 m/s^2).

To find the force of friction, we can use the equation Ff = uFn, where u is the coefficient of friction and Fn is the normal force, which is equal to the force of gravity in this case. The coefficient of friction depends on the surfaces in contact and can vary.

Putting all of this together, the equation for the net force becomes:

F = ma + mg sin(theta) + u(mg cos(theta))

Substituting in the given values, we get:

F = (6.5 kg)(1.61 m/s^2) + (6.5 kg)(9.81 m/s^2)sin(13 degrees) + u(6.5 kg)(9.81 m/s^2)cos(13 degrees)

Simplifying, we get:

F = 10.49 N + 14.80 N + 6.74u N

Since there are two variables (F and u), we cannot solve for a specific value. However, we can use this equation to find the minimum value of F needed for the cart to accelerate at 1.61 m/s^2. We can also vary the coefficient of friction to see how it affects the required force.