A long thin solid rod lies along the positive x-axis. One end is at x = 1.50 m and the other at x = 3.70 m. The linear mass density is A = ax3 + bx, where A is measured in kg/m, and the constants have thefollowing values: a = 1.60 kg/m4 and b = 2.80 kg/m². Determine the total mass of the rod.Submit Answer Tries 0/10Calculate the x-coordinate of the center of the mass for this rod.Submit Answer Tries 0/10

Answered: A long thin solid rod lies along the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 49PQ

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In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2 = 0.850 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. (b) Find the angular speed of the pulley at the same moment. Figure P10.40
A solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm, what is the tension in the wire?
A uniform rod has mass m and length L. One end of the rod is attached to a fixed point O by a hinge and an additional force F is applied to the other end of the rod in the direction shown, perpendicular to the rod. Given that the rod is in mechanical equilibrium, what is the magnitude of the applied force F, expressed as a numerical multiple of mg, where g is the magnitude of the acceleration due to gravity? Express your answer as a decimal number, specified to 3 significant figures
A uniform steel rod has mass 0.300 kg and length 40.0 cm and is horizontal. A uniform sphere with radius 8.00 cm and mass 0.900 kg is welded to one end of the bar, and a uniform sphere with radius 6.00 cm and mass 0.380 kg is welded to the other end of the bar. The centers of the rod and of each sphere all lie along a horizontal line. How far is the center of gravity of the combined object from the center of the rod?
A uniform rod is 2.00 m long and has mass 1.80 kg. A 2.40 kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite object to be 1.20 m from the left-hand end of the rod?
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.156 mrh=0.156 m and mass 5.08 kg5.08 kg, and two thin crossed rods of mass 7.80 kg7.80 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0525 mtd=0.0525 m thick, made out of a material with a density of 8290 kg8290 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?
The upper surface of a cube of gelatin, 5.0 cm on a side, is displaced by 0.64 cm by a tangential force. If the shear modulus of the gelatin is 940 Pa, what is the magnitude of the tangential force?
A solid cylinder has length L = 14 cm and radius R = 2 cm. The center of one face of the cylinder is located at the origin and the cylinder’s axis lies along the positive x-axis. The mass density of the cylinder varies along its length and is given by the function: ρ(x) = Ax2 + Bx + C, where A = 13.5 kg/m5, B = 5.2 kg/m4, and C = 14.2 kg/m3. Consider a thin slice of the cylinder that is a disk located at distance x from the origin and having thickness dx. Enter an expression for the mass of this disk in terms of the defined quantities and dx. Integrate the expression you entered in part (a) and enter an expression for the mass of the whole cylinder in terms of the defined quantities. Calculate the mass of the cylinder, in grams. Enter an expression for the location of the cylinder’s center of mass along the x-axis, in terms of the defined quantities. Calculate the location of the cylinder’s center of mass along the x-axis, in centimeters.
A uniform horizontal beam 5.00 m long and weighting 3.03 102 N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal (Figure (a)). If a person weighing 6.05 102 N stands 1.60 m from the wall, find the magnitude of the tension in the cable and the force exerted by the wall on the beam. T = N Rx = N Ry = N Even if we selected some other axis for the torque equation, the solution would be the same. For example, if the axis were to pass through the center of gravity of the beam, the torque equation would involve both T and Ry. Together with Equations (1) and (2), however, the unknowns could still be found—a good exercise. In this example, notice the steps of the Problem-Solving Strategy could be carried out in the explicit recommended order.QUESTION What happens to the tension in the cable if the man in Figure (a) moves farther away from the wall? The tension would…
A uniform steel rod has mass 0.300 kgkg and length 40.0 cmcm and is horizontal. A uniform sphere with radius 8.00 cmcm and mass 0.900 kgkg is welded to one end of the bar, and a uniform sphere with radius 6.00 cmcm and mass 0.680 kgkg is welded to the other end of the bar. The centers of the rod and of each sphere all lie along a horizontal line. How far is the center of gravity of the combined object from the center of the rod? Express your answer with the appropriate units. Enter negative value if the center of gravity is toward the 0.900 kgkg sphere and positive value if the center of gravity is toward the 0.680 kgkg sphere.
overhead view of a rigid rod that turnsabout a vertical axle until the identical rubber stoppers A and B are forced against rigid walls at distances rA = 7.0 cm and rB = 4.0 cmfrom the axle. Initially the stoppers touch the walls without beingcompressed.Then force of magnitude 220 N is applied perpendicularto the rod at a distance R = 5.0 cm from the axle.Find the magnitudeof the force compressing (a) stopper Aand (b) stopper B.
In the figure below, the hanging object has a mass of m1 = 0.350 kg; the sliding block has a mass of m2 = 0.780 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is μk = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. m/s(b) Find the angular speed of the pulley at the same moment. rad/s

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