An object with a mass of #6 kg# is on a surface with a kinetic friction coefficient of # 8 #. How much force is necessary to accelerate the object horizontally at # 19 m/s^2#?

Answer 1

# 584.4 N#

The forces are marked on the diagram;

#F = # Friction
#R = # Reaction from the surface
#D = # Driving Force (our unknown)
Applying NSL vertically downwards:

# 6g - R = 0 #
# :. R = 6g #
# :. R = 58.8N #

Applying NSL horizontally:

# D - F = (6)(19) #
# :. D = 114 + F #
# :. D = 114 + muR #
# :. D = 114 + (8)(58.8) #
# :. D = 114 + 470.4 #
# :. D = 584.4 N#

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Answer 2

Nathan Ashcroft

The force necessary to accelerate the object horizontally at 19 m/s^2 is 138 Newtons.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.