Homework Help - Physics Question. Story problem dealing with frictional force, velocity, and acceleration...?

Question

At time zero a 0.27 kg book is sliding at 10.0 m/s, left. Bill is pushing the book with a force of 3.4 N, left, but the acceleration is 4.0 m/s^2, right. Calculate (a) the friction force (mag. & dir.) and (b) the velocity (mag. & dir.) after 1.5 s.

I've drawn a diagram but I don't understand how to solve. I'm not sure which equations to use or anything like that.

Yeah, this is all theoretically speaking. I have four problems that are all similar (velocity and force to the left with acceleration to the right). Can you explain it anymore though? Also, if you could tell me more about the equations you use... I'd be very appreciative. I'm a very math-y person and I like equations a lot. heh.

Answer 1

Am I missing something here? I am agreeing with arbiter above in theory but that would require a frictional force of 4.48 N, hard to acheive with a 2.65N book on earth.

OK, since the question is still open, I will explain how I would solve this problem. For this problem to work, I will agree that the weight of the book in Newtons is not required. In fact, the gravity would have to be at least 16.59m/s^2 and coefficient of friction would be 1.0, but again, that doesn't come in to play here.

The book is moving to the left at 10m/s, being pushed to the left with a force of 3.4 N, but it is accelerating to the right at 4 m/s^2. Therefore the force of friction must be greater than the force that Bill is pushing with.

Now, calculate what force would be required to accelerate the book at 4 m/s^2.

F=ma , where m = 0.27kg and a = 4 m/s
F=1.08N

Therefore, the resultant force of the friction must be equal to Bill's force + 1.08N or 4.48 N. Since it is in opposition to Bill's force, it is to the right.

Frictional Force = 4.48 N to the right

For velocity at 1.5s, use Vx = Vinit + a*t
Velocity initial = -10 m/s (left is negative, right positive)
a = 4 m/s^2 (positive since it is to the right
t=1.5s

velocity = -10 m/s +4m/s^2 * 1.5s
Therefore,
velocity = -4 m/s or 4 m/s to the left

Hope that helps.

Answer 2

The fact that the acceleration is still to the right means that the pushing to the left cannot overcome the frictional force. Therefore the frictional force must be (4 m/s^2)*0.27 kg + 3.4N, all to the right

Answer 3

s[one million] = u[one million]t + zero.5a[one million]t^two = two.five x 10 + three.zero x one hundred = 325 m s[two] = five x 10 + three.zero x one hundred = 350 m Separation 25 m v[one million] = u[one million] + at = two.five + three.zero x 10 = 32.five m/s v[two] = five + three.zero x 10 = 35 m/s