Final speed after dragging crate

[drewdiddy]

Homework Statement

A 96 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15m the floor is frictionless and for the next 15 m the coefficient of friction is .25. What is the final speed of the crate?

Homework Equations

Change in K = Work
E + Ffr * d = 0
1/2mv^2-1/2mv^2 + F(fr) d

The Attempt at a Solution

I broke this up into two steps. The first 15 m I took the Work done, set it equal to 1/2mv^2 and got the velocity for the beginning of the second reference frame . Somethings not working though because I get the incorrect answer. Am I setting this up incorrectly?

 

[needlottahelp]

Umm..I don't think you need to calculate anything for the Work. I don't see the need for the work. Find the acceleration using F=ma and put it into the correct kinematic equations to find the Vf of the first 15 m. Then take into account friction for the second have and use the same kinematic equation with the Vi being the Vf of the first 15 m.

 

[baba89]

I would approach this problem by first analyzing the forces acting on the crate. The horizontal force of 350 N will accelerate the crate, while the coefficient of friction will act in the opposite direction, causing a deceleration. This means that the crate will experience a net force of 350 N - (96 kg * 9.8 m/s^2 * 0.25) = 326.4 N.

Next, I would use the equation F=ma to calculate the acceleration of the crate. a = F/m = 326.4 N / 96 kg = 3.4 m/s^2.

Using the kinematic equation v^2 = u^2 + 2as, where u is the initial velocity (0 m/s) and s is the distance traveled (15 m), we can solve for the final velocity at the end of the first reference frame: v = √(0^2 + 2 * 3.4 m/s^2 * 15 m) = 7.35 m/s.

For the second reference frame, we can use the same equation with the new distance of 15 m and the same acceleration of 3.4 m/s^2, but with a negative sign to represent the deceleration caused by friction. This gives us a final velocity of v = √(7.35^2 + 2 * (-3.4 m/s^2) * 15 m) = 5.63 m/s.

Therefore, the final speed of the crate is 5.63 m/s after being dragged a total distance of 30 m.