Eng1010 - Sample Test 2 1

1. A 54 kg crate with c.g. G2 rests on the 27 kg pickup tailgate with c.g. G1. Determine the tensionin the two restraining cables, one of which is shown (AB), and the x, y components of the reactionsat the two supports O. Note: there are two restraining cables and two pivot points O. The crate islocated midway between the two support cables (i.e. into the page). Record your numerical answersin 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 theincline. The mass of the mower with the attached grass bag is 50 kg with mass center at G. If θ = 15◦,determine the magnitudes of the force ~P , and the nomal forces ~NB and ~NC under each pair of wheelsat B and C. Neglect friction. (P = 127 N, NB = 213.8 N, NC = 260 N)

3. The figure shows a roll-off truck ramp for discharging loaded containers. The 120,000 kg loaded con-tainer has mass center at G, and is supported by two wheels at A and two wheels at B. In the positionshown, the pair of wheels at A are blocked, and the brakes of the truck are applied to prevent move-ment. Determine the reactions for each wheel at A and B. Write the reactions as vectors (i.e. ~A = A],~B = B]). ( ~A = 465.9∠71.7◦ kN, ~B = 206.7∠135◦ kN)

Eng1010 - Sample Test 2 2

4. The rubber-tired four wheel drive tractor has a mass of 13,500 kg with center of mass at G and is usedfor pushing or pulling heavy loads. Determine the maximum load P which the tractor can pull at aconstant speed of 5 km/h up the 15% grade if the driving force exerted by the ground on each of itsfour wheels is 80% of the normal force under that wheel. What are the normal forces under each pairof wheels (i.e. both wheels at each location)? (P = 85.14 kN, NA = 6.27 kN, NB = 124.70 kN)

5. The riding power mower has mass of 200 kg with center of mass at G1. The operator has mass 90 kgwith center of mass at G2. The mower and operator are travelling down a θ = 10◦ slope. To maintainthe speed of the mower constant, the brakes are applied to the rear wheels only. Determine the brakingforce, FB , required to maintain a constant speed, and the normal forces acting on the front, NF , andrear, NR, pairs of wheels. Note: You may use the given figure as your FBD, and all dimensions are inmeters. (FB = 494 N, NF = 996.5 N, NR = 1805.2 N)

Eng1010 - Sample Test 2 3

6. You are reversing your 1500 kg front wheel drive car up a 10◦ incline at a constant speed. Determinethe magnitudes of the driving force on the front tires, FA, and the normals at the front and rear pairsof tires, NA and NB , respectively. The rear wheels roll freely, and neglect the mass of the wheels andtires. (FA = 2555.2 N, NA = 8645.8 N, NB = 5845.6 N)

7. The hoist supports the engine of mass m1 = 100 kg. The uniform beam GFE has mass m2 = 10 kgwith center of gravity located at its geometric center. Determine the force ~H in the hydraulic cylinderattached at F and the force ~E acting on beam GFE at pin connection E. ( ~H = 1628.6∠108.4◦ N,~B = 694.5∠317.9◦ N)

Eng1010 - Sample Test 2 4

8. The jib crane shown below supports a load of 10 kN. The beam AB is a uniform cross-section I-beamwith mass of 100 kg per meter of length. The beam is pin-connected at A and is supported by a cableattached at B. Determine the magnitude of the tension, ~T , in the supporting cable and the magnitudeof the reaction force, ~A, of the pin connection at A. You may assume the cable connection point at Bis at the upper surface of beam AB. (T = 19.867 kN, A = 19.146 kN)

9. The portable floor crane in an automotive shop is lifting an engine of weight 500 lb. The weight of theboom is 80 lb and its center of mass is located at B. The boom is pin-connected to the frame at C andto a hydraullic cylinder at B. Determine the magnitude of the force exerted on the boom at B by thehydraulic cylinder, and the force of pin C on the boom. Neglect the weight of the hydraulic cylinder.(| ~B| = 2095.8 (lb), |~C| = 1538.8 (lb))

Eng1010 - Sample Test 2 5

10. The loader has a mass m1 = 1500 kg with center of mass G1. The load in the bucket has massm2 = 250 kg with center of mass G2. After a long overnight shift the loader is resting on the θ = 15◦

incline. If brakes are applied to the two front wheels only, determine the magnitude of the normals ateach front tire (NA) and each rear tire (NB), and the magnitude of the braking force required at eachfront tire (FA). Notes: (1) The heights of G1 and G2 are 0.5 m and 0.7 m, respectively, measuredperpendicular to the ground; and (2) To save time you can use the given figure for your free bodydiagram. (NA = 3409.1 (N), NB = 4882.2 (N), FA = 2221.6 (N))