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 #?

1 Answer
Apr 17, 2018

Answer:

W = 87.21 J

Explanation:

The ramp is at an angle of 75 degrees, so to find the force of gravity pulling it down, we find:

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

Now, to find the for of the opposing friction force, we find:

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

In the case of a ramp, normal force is only the component of gravity perpendicular to the ramp, so:

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

# F_"F" = 2 * 5.07 = 10.14 N #

Now we can use F_"net" = ma to find set up total force. And assuming the minimum work is wanted, a (an subsequently 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 #

Now to find work, use W= f*d cos(theta), where theta will be set to 0 as we assume the force is applied in the same direction of the ramp.

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