Eng1010 - Sample Test 2 1

Eng1010 - Sample Test 2
1. A 54 kg crate with c.g. G2 rests on the 27 kg pickup tailgate with c.g. G1 . Determine the tension
in the two restraining cables, one of which is shown (AB), and the x; y components of the reactions
at the two supports O. Note: there are two restraining cables and two pivot points O. The crate is
located midway between the two support cables (i.e. into the page). Record your numerical answers
in the table below (indicating directions). (FAB = 578 N, Ox = 415:8 N , Oy = 8:4 N #)
2. A man pushes the lawn mower up the incline at constant speed with a force P~ which is parallel to
the incline. The mass of the mower with the attached grass bag is 50 kg with mass center at G. If
~ B and N
~ C under each pair
= 15 , determine the magnitudes of the force P~ , and the nomal forces N
of wheels at B and C. Neglect friction. (P = 127 N, NB = 213:8 N, NC = 260 N)
3. The …gure shows a roll-o¤ truck ramp for discharging loaded containers. The 120; 000 kg loaded
container has mass center at G, and is supported by two wheels at A and two wheels at B. In the
position shown, the pair of wheels at A are blocked, and the brakes of the truck are applied to prevent
movement. Determine the reactions for each wheel at A and B. Write the reactions as vectors (i.e.
~ = A], B
~ = B]). (A
~ = 465:9\71:7 kN, B
~ = 206:7\135 kN)
Eng1010 - Sample Test 2
4. The rubber-tired four wheel drive tractor has a mass of 13; 500 kg with center of mass at G and is used
for pushing or pulling heavy loads. Determine the maximum load P which the tractor can pull at a
constant speed of 5 km= h up the 15% grade if the driving force exerted by the ground on each of its
four wheels is 80% of the normal force under that wheel. What are the normal forces under each pair
of wheels (i.e. both wheels at each location)? (P = 85:14 kN, NA = 6:27 kN, NB = 124:70 kN)