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A uniform 4.0-m plank weighing 200.0 N rests against the corner of a wall, as shown below. There is no friction at the point where the plank meets the corner. (a) Find the forces that the corner and the floor exert on the plank. (b) What is the minimum coefficient of static friction between the floor and the plank to prevent the plank from slipping?

Figure shows a uniform plank that rests against a corner the corner of a wall. Part of the plank from the floor to the corner of the wall is 3.0 m long, 1.0 m long part of plank is above the wall. Distance between the part of the plank that touches the ground and the corner of the wall is 1.5 m.

a. at corner 66.7 N at 30 ° with the horizontal; at floor 192.4 N at 60 ° with the horizontal; b. μ s = 0.577

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A 40-kg boy jumps from a height of 3.0 m, lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant deceleration. If the total cross-sectional area of the bones in his legs just above his ankles is 3.0 cm 2 , what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than 1.7 × 10 8 Pa . Is the boy in danger of breaking his leg?

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Two thin rods, one made of steel and the other of aluminum, are joined end to end. Each rod is 2.0 m long and has cross-sectional area 9.1 mm 2 . If a 10,000-N tensile force is applied at each end of the combination, find: (a) stress in each rod; (b) strain in each rod; and, (c) elongation of each rod.

a. 1.10 × 10 9 N/m 2 ; b. 5.5 × 10 −3 ; c. 11.0 mm, 31.4 mm

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Two rods, one made of copper and the other of steel, have the same dimensions. If the copper rod stretches by 0.15 mm under some stress, how much does the steel rod stretch under the same stress?

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Challenge problems

A horizontal force F is applied to a uniform sphere in direction exact toward the center of the sphere, as shown below. Find the magnitude of this force so that the sphere remains in static equilibrium. What is the frictional force of the incline on the sphere?

Figure shows a sphere of radius R and mass M that placed at the side of the triangle forming angle Theta with the ground. Force F is applied to the sphere.

F = Mg tan θ ; f = 0

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When a motor is set on a pivoted mount seen below, its weight can be used to maintain tension in the drive belt. When the motor is not running the tensions T 1 and T 2 are equal. The total mass of the platform and the motor is 100.0 kg, and the diameter of the drive belt pulley is 16.0 cm. when the motor is off, find: (a) the tension in the belt, and (b) the force at the hinged platform support at point C . Assume that the center of mass of the motor plus platform is at the center of the motor.

Figure shows a motor set on a pivoted mount. The center of the motor is 25 cm above and 30 cm to the right from the support point C. Tension T1 forms a 40 degree angle with the line parallel to the ground. Tension T2 forms a 15 degree angle with the line parallel to the ground.
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Two wheels A and B with weights w and 2 w , respectively, are connected by a uniform rod with weight w /2, as shown below. The wheels are free to roll on the sloped surfaces. Determine the angle that the rod forms with the horizontal when the system is in equilibrium. Hint: There are five forces acting on the rod, which is two weights of the wheels, two normal reaction forces at points where the wheels make contacts with the wedge, and the weight of the rod.

Figure shows the wheels A and B connected by the rod and located at the opposite side of the right angle triangle. Side at which wheel A is located forms a 60 degree angle with the line parallel to the ground. Side at which wheel B is located forms a 30 degree angle with the line parallel to the ground.

with the horizontal, θ = 42.2 ° ; α = 17.8 ° with the steeper side of the wedge

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Weights are gradually added to a pan until a wheel of mass M and radius R is pulled over an obstacle of height d , as shown below. What is the minimum mass of the weights plus the pan needed to accomplish this?

Figure shows a pan connected to the wheel by a wire. Wire has mass M and radius R. An obstacle of height D separates wheel from the pan.
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In order to lift a shovelful of dirt, a gardener pushes downward on the end of the shovel and pulls upward at distance l 2 from the end, as shown below. The weight of the shovel is m g and acts at the point of application of F 2 . Calculate the magnitudes of the forces F 1 and F 2 as functions of l 1 , l 2 , mg , and the weight W of the load. Why do your answers not depend on the angle θ that the shovel makes with the horizontal?

Figure shows a gardener lifting a shovel full of ground with both hands. Force F1 is applied to the back hand. Force F2 is applied to front hand. Force w is applied to the front of shovel with ground. Distance between the back hand and front of shovel is l1. Distance between the back and front hands is l2. Angle between the shovel and line parallel to the ground is theta.

W ( l 1 / l 2 1 ) ; W l 1 / l 2 + m g

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A uniform rod of length 2R and mass M is attached to a small collar C and rests on a cylindrical surface of radius R , as shown below. If the collar can slide without friction along the vertical guide, find the angle θ for which the rod is in static equilibrium.

Figure shows a uniform rod of length 2R and mass that M is attached to a small collar C and rests on a cylindrical surface of radius R. Angle between the collar and the line parallel to the ground is theta.
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The pole shown below is at a 90.0 ° bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is 4 . 0 0 × 1 0 4 N , at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the strength of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0 ° with the vertical. The guy wire is in the opposite direction of the bend.

Figure shows a pole to which two forces T and force Tgw are applied. There is a 90 degree angle between two T forces. There is an 80 degree angle between the plane T forces are applied anf the pole. There is a 30 degree angle between Tgw and the pole.

a. 1.1 mm; b. 6.6 mm to the right; c. 1.11 × 10 5 N

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Practice Key Terms 6

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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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