Finding acceleration of an object on a horizontal surface

[Sunchild16]

Homework Statement

The coefficients of static and kinetic friction between a 59 kg box and a horizontal surface are 0.66 and 0.37, respectively.

(a) What is the acceleration of the object if a 330 N horizontal force is applied to the box?

(b) What is the acceleration if the applied force is 485 N

Homework Equations

F=ma, coefficent of friction equations

The Attempt at a Solution

I tried using the equations

but I am not really sure how they are supposed to be used

 

[renaldocoetz]

Is this applied to the box at rest? in that case the applied force has to be greater than the max Static Friction for the box to have any acceleration.

 

[tomcue]

to find the acceleration. Can you please clarify?

I would approach this problem by first identifying the relevant equations and variables. In this case, we are dealing with Newton's second law (F=ma) and the coefficients of friction. The given information tells us that the box has a mass of 59 kg and the coefficients of static and kinetic friction are 0.66 and 0.37, respectively. We are also given two different applied forces (330 N and 485 N).

To solve for the acceleration, we can use the formula F=ma, where F is the net force acting on the box, m is the mass of the box, and a is the acceleration. In this case, the net force is the applied force minus the force of friction. The force of friction can be calculated using the coefficients of friction and the normal force (which is equal to the weight of the box, mg).

(a) To find the acceleration when a 330 N force is applied, we can use the formula F=ma and set F=330 N. The force of friction can be calculated as μsN, where μs is the coefficient of static friction and N is the normal force. The normal force is equal to the weight of the box, which is mg. So, the force of friction in this case is μsmg. Plugging this into the formula F=ma and rearranging for a, we get a=(F-μsmg)/m. Substituting in the given values, we get a=(330-0.66(59)(9.8))/59=2.89 m/s^2.

(b) To find the acceleration when a 485 N force is applied, we can follow the same steps as above, but now the force of friction is μkN, where μk is the coefficient of kinetic friction. So, the formula for acceleration is a=(F-μkmg)/m. Substituting in the given values, we get a=(485-0.37(59)(9.8))/59=3.41 m/s^2.

In summary, to find the acceleration of an object on a horizontal surface, we can use the formula F=ma and take into account the force of friction, which can be calculated using the coefficients of friction and the normal force.