A bax with a mass of 5 kg is resting on a horizontal surface without friction. O

Question

A bax with a mass of 5 kg is resting on a horizontal surface without friction. One force of 12 Newtons is applied straight downward. Another force of 6 Newtons is applied to the left Lastly, a force of is applied to it at an angle of 45 degrees above the horizontal (ex direction). (See sketch below) The third force is just barely enough to begin to lift the box off the ground. How far does the object slide 2.2 seconds affter the forces are applied in meters? Fs Fi A mass of 6 kg is placed on a frictionless incline which is inclined at 45 degrees. A force of 22 Newtons is applied to it directly up the incline and another force is applied to the left (see sketch) Due to these forces, the amount of the normal force on the mass is 149 Newtons. The mass is at rest at the bottom of the incline and after the forces have been applied for 2.6 seconds, the mass has moved all the way up the incline What is the length (not height) of the incline in meters? The mass never comes off the incline. Fi F2

Explanation / Answer

N = 0,

in vertical, Fnet= F3 sin45 - F1 - m g = 0

F3 = ( 12 + 5x9.8 ) / sin45 = 86.26 N

In horizontal,

Fnet = 86.26cos45 - 6 = 5 a

a = 11 m/s^2

v = v0 + a t

v = 0 + (11 x 2.2) = 24.2 m/s ....Ans

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perpendicular to the incline,

N - m g cos45 - F2 sin45 = 0

149 = (6 x 9.8)cos45 + F2 sin45

F2 = 152 N

along the incline,

Fnet= F1 + F2 cos45 - m g sin45 = 6 a

a = 14.6 m/s^2

v = 0 +(14.6 x 2.6) = 38 m/s

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