Two stacked boxes are sliding along an ice rink with an initial velocity of v 0

Question

Two stacked boxes are sliding along an ice rink with an initial velocity of v0 to the right. You are trying to stop the boxes so you exert a force Fy1 on the top box as indicated in the figure.

The magnitude of the force that you exert is variable, and follows the equation:

with F0 and b constants, and t the time since you began exerting the force.
Because the boxes are sliding on ice, the friction between box 2 and the ground is negligible. There is friction between the two boxes, and they are observed to accelerate together as you exert the force to slow them down.

Note: This problem will be much easier if you solve everything symbolically before you substitute in the values for the parameters.


Use the following values for the parameters:

b)Determine the total time, tf , that it takes you to stop the blocks.

I am completely stuck on this problem, any help would be appreciated!

Two stacked boxes are sliding along an ice rink with an initial velocity of v0 to the right. You are trying to stop the boxes so you exert a force Fy1 on the top box as indicated in the figure. The magnitude of the force that you exert is variable, and follows the equation: Fy1=F0e^-bt with F0 and b constants, and t the time since you began exerting the force. Because the boxes are sliding on ice, the friction between box 2 and the ground is negligible. There is friction between the two boxes, and they are observed to accelerate together as you exert the force to slow them down. This problem will be much easier if you solve everything symbolically before you substitute in the values for the parameters.Use the following values for the parameters: m1=8 9 kg m2=4 7 kg phi=25 8 F0=107 N b=018 s^-1 t1=2.897 s v0=8.1 m s

Explanation / Answer

a = -sin? F/m = sin? Fo/(m1+m2) e^(-bt)

a = (-0.3518)*(112/(8+4.4)) * e^(-0.14*4.29)

a = -1.74 m/s2

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