Question

Starting from rest, a 4.10-kg block slides 2.10 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is (a) Determine the work done by the force of gravity. J(b) Determine the work done by the friction force between block and incline. J(c) Determine the work done by the normal force. J(d) Qualitatively, how would the answers change if a shorter ramp at a steeper angle were used to span the same vertical height

Answer 1

mass of the block = 4.10 Kg

distance of slide = 2.1 m

angle of inclination = 30.0°

μ_k be equal to 0.436

a) Work done by the gravity

`W = \mu_k m g sin \theta * d`

`W =0.436 * 4.1 * 9.8 *  sin 30^0 * 2.1`

`W =19.39\ J`

b) Work done due to friction =
`\mu N L`

=
`-\mu m g cos \theta L`

=
`-0.436 * 4.1 * 9.8 * cos 30^0 * 2.1`

= -31.86 J

c) work done by the normal force = 0 J

Since normal force and displacement are perpendicular to each other

d) for steeper angle

sin θ value is high

cos θ value is less

work done by gravity on steeper angle is more

work done by frictional force will on steeper angle is less

work done by normal force is zero