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- Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.100 μm, what is the length of the fiber?You use a millimeter ruler to measure the height of a rail curb. The bottom of the ruler is resting on the table. The place where the height measurement is taken is a little curved, so it is difficult to identify very precisely where the measurement should be taken. Also, it's a bit tricky to make sure the ruler is perfectly vertical (it might be leaning forward or backward a bit). When you take the measurement, you measure 12.9 mm. By moving the ruler a little, you are confident that the correct measurement is somewhere between 12.7 mm and 13.3 mm. Indicate the value that you will record in your logbook, as well as the uncertainty that you will attribute to it. Give your answers in mm.
- You use a millimeter ruler to measure the height of a rail curb. The bottom of the ruler is resting on the table. The place where the height measurement is taken is a little curved, so it is difficult to identify very precisely where the measurement should be taken. Also, it's a bit tricky to make sure the ruler is perfectly vertical (it might be leaning forward or backward a bit). When you take the measurement, you measure 12.9 mm. By moving the ruler a little, you are confident that the correct measurement is somewhere between 12.7 mm and 13.3 mm. Indicate the value that you will record in your logbook, as well as the uncertainty that you will attribute to it. Give your answers in mm. Warning: Keep at least 3 significant digits in your answers, even if it does not respect the rules of presentation of data in the laboratory.A 3.0 m long steel wire of radius 0.60 mm supports a weight of 50 N. By how much is the wire elongated because of this weight?A parking garage is designed for two levels of cars. To make more money, the owner decides to double the size of the gar- age in each dimension (length, width, and number of levels). For the support columns to hold up four floors instead of two, how should he change the columns’ diameter? (a) Double the area of the columns by increasing their diameter by a factor of 2. (b) Double the area of the columns by increasing their diameter by a factor of V2. (c) Quadruple the area of the columns by increasing their diameter by a factor of 2. (d) Increase the area of the columns by a factor of 8 by increasing their diameter by a factor of 2V2. (e) He doesn't need to increase the diameter of the columns.
- The bones of the forearm (radius and ulna) are hinged to the humerus at the elbow. The biceps muscle connects to the bones of the forearm about 2.15 cm beyond the joint. Biceps muscle Assume the forearm has a mass of 2.25 kg and a length of 0.425 m. When the humerus and the biceps are nearly vertical and the forearm is horizontal, if a person wishes to Humerus hold an object of mass 6.55 kg so that her forearm remains motionless, what is the force exerted by the biceps muscle? Radius Elbow. Ulna force: N HandTwo wires A and B are of the same length. Their diameters are in the ratio 1:2 and the Young's modulii are in ratio 2 : 1. If they are pulled by the same force, then elongations will be in ratioProblem 7 *3-9. The σ-e diagram for a collagen fiber bundle from which a human tendon is composed is shown. If a segment of the Achilles tendon at A has a length of 6.5 in. and an approximate cross-sectional area of 0.229 in², determine its elongation if the foot supports a load of 125 lb, which causes a tension in the tendon of 343.75 lb. σ (ksi) 4.50 3.75 3.00 2.25 1.50 0.75 0.05 0.10 125 lb € (in./in.) A
- A force stretches a (first) wire by 2mm. This wire is made of an unknown material and has a 1.2cm diameter and 3.5cm length. A second wire of the same material has the same cross-section and three times the length. How far will it be stretched by the sameforce?When using a ladder, it is important to place it against a wall at a safe angle. A ladder could tip over backwards if the angle is too large or the ladder could slide down the wall if the angle is too small. For a ladder to be placed at a safe angle, the ratio of the working length (how far you climb the ladder) to how far the ladder is from the wall should be 4 : 1. What angle should we place place our ladders at so that they are safe when we use them?Y Figure Fw 40° CG Ymg FT 1 of 1 Calculate the tension Fr in the wire that supports the 42 kg beam shown in the figure(Figure 1). Express your answer using two significant figures. Fr= 320 N Submit ✓ Correct Part B Calculate the magnitude of the force Fw exerted by the wall on the beam. Express your answer using two significant figures. Fw: || Previous Answers Submit Part C VO ΑΣΦ A Request Answer Ċ ? N