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A painter climbs a ladder. Is the ladder more likely to slip when the painter is near the bottom or near the top?

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Problems

A uniform plank rests on a level surface as shown below. The plank has a mass of 30 kg and is 6.0 m long. How much mass can be placed at its right end before it tips? ( Hint: When the board is about to tip over, it makes contact with the surface only along the edge that becomes a momentary axis of rotation.)

Figure schematic drawing of uniform plank rests on a level surface. Part of the plank that is 4.2 meters long is supported by the plank. Part of the plank that is 1.8 meters long is hanging over it.
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The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?

Figure is a schematic drawing of two boys on the seesaw. One boy sits on the edge of the seesaw three meters from the center. Another boys sits at the opposite edge of the seesaw, five meters from the center.

40 kg

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In order to get his car out of the mud, a man ties one end of a rope to the front bumper and the other end to a tree 15 m away, as shown below. He then pulls on the center of the rope with a force of 400 N, which causes its center to be displaced 0.30 m, as shown. What is the force of the rope on the car?

Figure is a schematic drawing that shows a rope tied to the front bumper and the other end to a tree 15 m away. A force of 400 N is applied to the center of the rope and causes it to get displaced 0.30 m.
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A uniform 40.0-kg scaffold of length 6.0 m is supported by two light cables, as shown below. An 80.0-kg painter stands 1.0 m from the left end of the scaffold, and his painting equipment is 1.5 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables and the mass of the equipment.

Figure is a schematic drawing of a man standing at the left side and the bucket placed at the right side of a scaffold.

right cable, 444.3 N; left cable, 888.5 N; weight of equipment 156.8 N; 16.0 kg

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When the structure shown below is supported at point P , it is in equilibrium. Find the magnitude of force F and the force applied at P . The weight of the structure is negligible.

Figure shows the distribution of forces applied to point P. Force of 2000 N, two meters to the left of the point P, moves it downwards. Force F, two meters to the left and two meters above of the point P, moves it to the right. Force of 1000 N, two meters to the right and three meters below of the point P, moves it to the left.
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To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.

784 N, 376 N

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A uniform horizontal strut weighs 400.0 N. One end of the strut is attached to a hinged support at the wall, and the other end of the strut is attached to a sign that weighs 200.0 N. The strut is also supported by a cable attached between the end of the strut and the wall. Assuming that the entire weight of the sign is attached at the very end of the strut, find the tension in the cable and the force at the hinge of the strut.

Figure is a schematic drawing of a sign which hangs from the end of a uniform strut. The strut forms a 30 degree angle with the cable tied to the wall above the left end of the strut.
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The forearm shown below is positioned at an angle θ with respect to the upper arm, and a 5.0-kg mass is held in the hand. The total mass of the forearm and hand is 3.0 kg, and their center of mass is 15.0 cm from the elbow. (a) What is the magnitude of the force that the biceps muscle exerts on the forearm for θ = 60 ° ? (b) What is the magnitude of the force on the elbow joint for the same angle? (c) How do these forces depend on the angle θ ?

Figure is a schematic drawing of a forearm rotated around the elbow. A 5 kilogram ball is held in the palm. The distance between the elbow and the ball is 35 centimeters. The distance between the elbow and the biceps muscle, which causes a torque around the elbow, is 4 centimeters. Forearm forms a theta angle with the upper arm.

a. 539 N; b. 461 N; c. do not depend on the angle

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The uniform boom shown below weighs 3000 N. It is supported by the horizontal guy wire and by the hinged support at point A . What are the forces on the boom due to the wire and due to the support at A ? Does the force at A act along the boom?

Figure is a schematic drawing of a 2000 N weight that is supported by the horizontal guy wire and by the hinged support at point A. Hinged support forms a 45 degree angle with the ground.
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The uniform boom shown below weighs 700 N, and the object hanging from its right end weighs 400 N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on the hinge act along the boom?

Figure is a schematic drawing of a 400 N weight that is by a cable and by a hinge at the wall. Hinge forms a 20 degree angle with the line perpendicular to the wall. Cable forms a 45 degree angle with the line perpendicular to the wall.

tension 778 N; at hinge 778 N at 45 ° above the horizontal; no

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A 12.0-m boom, AB , of a crane lifting a 3000-kg load is shown below. The center of mass of the boom is at its geometric center, and the mass of the boom is 1000 kg. For the position shown, calculate tension T in the cable and the force at the axle A .

Figure is a schematic drawing of a crane lifting a 3000-kg load. Arm of a crane forms a 30 degree angle with the line parallel to the ground. Cable supporting load forms a 10 degree angle with the arm.
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A uniform trapdoor shown below is 1.0 m by 1.5 m and weighs 300 N. It is supported by a single hinge (H), and by a light rope tied between the middle of the door and the floor. The door is held at the position shown, where its slab makes a 30 ° angle with the horizontal floor and the rope makes a 20 ° angle with the floor. Find the tension in the rope and the force at the hinge.

Figure is a schematic drawing of a trapdoor that is 1.0 m by 1.5 m. Door is supported by a single hinge labeled H, and by a light rope tied between the middle of the door and the floor. The door makes a 30 degree angle with the floor and the rope makes a 20 degree angle with the floor.

1500 N; 1620 N at 30 °

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A 90-kg man walks on a sawhorse, as shown below. The sawhorse is 2.0 m long and 1.0 m high, and its mass is 25.0 kg. Calculate the normal reaction force on each leg at the contact point with the floor when the man is 0.5 m from the far end of the sawhorse. ( Hint: At each end, find the total reaction force first. This reaction force is the vector sum of two reaction forces, each acting along one leg. The normal reaction force at the contact point with the floor is the normal (with respect to the floor) component of this force.)

Figure is a schematic drawing of a man walks on a sawhorse. Each side of the sawhorse is supported by two connected legs. There are 60 degree angles between the legs.
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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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