Question

A couch of mass 210kg is being pushed across the floor with an applied force of 4100N. The coefficient of connect friction between the couch and the floor is 0.38. Find the acceleration of the couch.

Answer 1

Since it's flat, normal force (Fn) would be equal to mg, which is 2100N. Since Ff=mu*Fn, Ff=798N. So the net force would be 4100N-798N which equals 3302N. Since f=ma, you can solve for a by f/m so a= 15.7 m/s^2 right?

Answer 2

Just making sure because I think the answer key I have is wrong and my answer is right.

Answer 3

kinetic* btw

Answer 4

seems right to me.

Answer 5

maybe they are using 9.8 for gravitational pull instead of the 10 you are using.

Answer 6

yeah idk how you got g = 10 when g = 9.81 roughly

Answer 7

My teacher has us use 10 for the sake of easy numbers

Answer 8

Thanks though

Answer 9

I tried using 9.8 and the answer was still way off. Their answer was 9.5

Answer 10

I think you should do this

4100N - 2100N = 2000 N

Divide 2000 N by the mass 210 kg to get 2000/210 = 9.5238

Answer 11

I'd get a second opinion since I'm not the best at physics

Answer 12

Well 2100 is the y component of mg and fn, but the object is stationary in the y direction.

Answer 13

The acceleration is in the x direction

Answer 14

hmm then I'm not sure

Answer 15

So it's the force exerted minus the force due to friction. And then since f=ma, you can divide the net force by m and get the acceleration.

Answer 16

Maybe that's the mistake that they made though

Answer 17

that is possible

Answer 18

Yeah it's just weird for the answer key to be wrong so I posted to see if I was forgetting something

Answer 19

One thing I learned over the years is to not always trust the answer in the back of a book.

With that said, the way you did the problem was correct and the correct answer is \(a\approx 15.8\,m/s^2\) (using \(g=9.8\,m/s^2\). They just forgot to multiply the normal force by the coefficient of friction when computing the net force acting on the couch.