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How much work does it take to push an object with a mass of #2 kg# up a #3 m# ramp, if the ramp has an incline of #(5pi)/12 # and a kinetic friction coefficient of #2 #?

Answer 1

W = 87.21 J

Since the ramp is angled at a 75-degree angle, the force of gravity dragging it down can be calculated as follows:

#F_"g" = mg*sin(theta) rArr F_"g" = 19.6 *sin(75) = 18.93 N#

In order to determine the opposing friction force's for, we now find:

# F_"F" = mu * F_"N"#

Only the portion of gravity perpendicular to a ramp constitutes normal force in this scenario, so:

# F_"N" = mg * cos(theta) = 5.07 N #
# F_"F" = 2 * 5.07 = 10.14 N #

Assuming the minimum amount of work is desired, we can now use F_"net" = ma to find the set up total force, and a (and consequently m) will be set to 0.

#F_"net" = ma# #F_"net" = cancel(m)(0)# #F_"net" = 0# # F_"a" - 18.93 - 10.14 = 0 # # F_"a" = 29.07 N #

W= f*d cos(theta) can now be used to find work; theta will be set to 0 because we are assuming that the force is applied in the ramp's direction.

# W = 29.07 * 3 cos(0) # #W = 29.07 * 3 # #W = 87.21 J #
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Answer 2

The work done to push the object up the ramp would be approximately 29.4 Joules.

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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.

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.

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.

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.

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