How Is Acceleration Calculated with Force and Friction Involved?

[badboyben03]

a 70 kg box s pulled by a 400 N force at an angle of 30 degrees to the horizontal. The force of kinetic friction is 75 N.

determine the acceleration.


heres what i did

first i found the x-component using (686)sin30 and it comes out to be 343.

Then i use the formula where the sum of forces = m*a and i plug in the numbers. 343=70a. divide by a and accelertaion is 4.9 m/s/s. is that right?

 

[jamesrc]

The horizontal component of the tension should be 400*cos(30)~346 N

The sum of forces in the x direction is then 346 - 75 = ma

solve for a ~ 3.9 m/s/s.

 

[M98Ranger]

Yes, your calculation is correct. The acceleration of the box is 4.9 m/s/s. You can also check your answer by using the formula for acceleration, a = Fnet/m. In this case, the net force is 400 N - 75 N = 325 N, and the mass is 70 kg. Plugging in these values, we get a = 325 N / 70 kg = 4.64 m/s/s, which is close to your answer of 4.9 m/s/s. Great job!