# 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 ?

Apr 17, 2018

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:

${F}_{\text{g" = mg*sin(theta) rArr F_"g}} = 19.6 \cdot \sin \left(75\right) = 18.93 N$

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

${F}_{\text{F" = mu * F_"N}}$

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

${F}_{\text{N}} = m g \cdot \cos \left(\theta\right) = 5.07 N$

${F}_{\text{F}} = 2 \cdot 5.07 = 10.14 N$

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.

${F}_{\text{net}} = m a$
${F}_{\text{net}} = \cancel{m} \left(0\right)$
${F}_{\text{net}} = 0$
${F}_{\text{a}} - 18.93 - 10.14 = 0$
${F}_{\text{a}} = 29.07 N$

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.

$W = 29.07 \cdot 3 \cos \left(0\right)$
$W = 29.07 \cdot 3$
$W = 87.21 J$