How fast must the astronaut\'s head be moving to experience this maximum acceler

Question

How fast must the astronaut's head be moving to experience this maximum acceleration? What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall? How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration? A box with mass 10.0 kg moves on a ramp that is inclined at an angle of 55.0 degree above the horizontal. The coefficient of Kinetic friction between the box and the ramp surface is mu_ k = 0.300. Calculate the magnitude of the acceleration of the box it you push on the box with a constant force F = 120.0 N that is parallel to the ramp surface and (a) directed down the ramp, moving the box down the ramp; (b) directed up the ramp, moving his box up the ramp. A factory worker pushes a 30.0-kg crate a distance to 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25 (a) What magnitude of force must the worker apply?

Explanation / Answer

Apply newton 's second law

F = ma = F(net)

also Ffr = kinetic frictional force = N [N is the normal reaction of the surface on the box = mgcos55°]

A.

along the incline equation is:

F + mgsin55° - Ffr = ma

=> 120 + 10gsin55° - 10gcos55° = ma

=> 200. 276 - 16.86 = 10a

=> a = 18.34 m/s² (down the ramp)

B.

equation is: F - mgsin55° - Ffr = ma

=> 120 - 10gsin55° - 10gcos55° = ma

=> 22.864 = 10a

or a = 2.286m/s² (up the ramp)

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