solid uniform ball with mass m and diameter dis supported against a vertical frictionless wall by a thin massless wire o ength L. a) Find the tension in the wire.
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- a) What is the mechanical advantage of a wheelbarrow, such as the one in Figure 9.24, if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is 55.0 kg? (c) What force does the wheel exert on the ground? Figure 9.24 (a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot IS the wheel's axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel's load) is less than the input force (from the hand nearest the load), because the Input is exerted closer to the pivot than is the outputThe forearm shown below is positioned at an angle 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 =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 ?(a) The "lead" in pencils is a graphite composition with a Young's modulus of about 1109 N/ m2. Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long. (b) Is the answer reasonable? That is, does it seem to be consistent with what you have observed when using pencils?
- At a museum, a 1300-kg model aircraft is hung from a lightweight beam of length 12.0 m that is free to pivot about its base and is supported by a massless cable (Fig. P14.38). Ignore the mass of the beam. a. What is the tension in the section of the cable between the beam and the wall? b. What are the horizontal and vertical forces that the pivot exerts on the beam? FIGURE P14.38 (a) From the free-body diagram, the angle that the string tension makes with the beam is = 55.0 + 18.0 = 73.0, and the perpendicular component of the string tension is FT sin73.0. Summing torques around the base of the rod gives (Eq. 14.2): =0:(12.0m)(1300kg)(9.81m/s2)cos55.0+FT(12.0m)sin73.0=0FT=(12.0m)(1300kg)(9.81m/s2)cos55.0(12.0m)sin73.0FT=7.65103N Figure P14.38ANS (b) Using force balance (Eq. 14.1): Fx=0:FHFTcos18.0=0FH=FTcos18.0=[(12.0m)(1300kg)(9.81m/s2)cos55.0(12.0m)sin73.0]cos18.0=7.27103NFy=0:FVFTsin18.0(1300kg)(9.81m/s2)=0 FV=FTsin18.0+(1300kg)gFV=[(12.0m)(1300kg)(9.81m/s2)cos55.0(12.0m)sin73.0]sin18.0+(1300kg)(9.81m/s2)FV=1.51104NQUESTION 1 Problem 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. a) Find the tension in the wire. Solution a) Let us first derive the expression for the tension. By Newton's First Law ΣF = ______ the components of force that makes this so is ΣF = T_____ -_____ = 0 Simplifying this results to T =________ g/_____(ϕ) Analyzing the figure above, we arrive at (ϕ) = sqrt(_____ 2 +______ ) / (_____ /_____ +_____ ) By substitution, we arrive at the following: T = (_____ + 2______ ) g / ( ______ sqrt (______ 2 +_____ ) ) If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm. The tension is equal to T = ________ 0.370 NA solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. a) Find the tension in the wire. Solution a) Let us first derive the expression for the tension. By Newton's First Law ΣF = ___ the components of force that makes this so is ΣF = T___ - ___ = 0 Simplifying this results to T = ___g/___(ϕ) Analyzing the figure above, we arrive at ___(ϕ) = sqrt(___2 + ___ ) / ( ___/___ + ___ ) By substitution, we arrive at the following: T = ___ ( ___ + 2___ ) g / ( ___sqrt ( ___2 + ___ ) ) If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm. The tension is equal to T = ___0.370 N
- 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. a) Find the tension in the wire. Solution a) Let us first derive the expression for the tension. By Newton's First Law ΣF = ______ the components of force that makes this so is ΣF = T ______ - ______ = 0 Simplifying this results to T = ______g/______(ϕ) Analyzing the figure above, we arrive at ______(ϕ) = sqrt( ______2 +______ ) / (______ /______ +______ ) By substitution, we arrive at the following: T = ______ ( ______ + 2 ______ ) g / ( ______ sqrt ( ______2 + ______ ) ) If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm. The tension is equal to T = ______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. a) Find the tension in the wire. Let us first derive the expression for the tension. By Newton's First Law ΣF = the components of force that makes this so is ΣF = T - = 0 Simplifying this results to T = g/(ϕ) Analyzing the figure above, we arrive at (ϕ) = sqrt( 2 + ) / ( / + ) By substitution, we arrive at the following: T = ( + 2 ) g / ( sqrt ( 2 + ) ) If the ball has a mass of 45 kg and diameter 32 cm, while the wire has a length of 30 cm. The tension is equal to T = 0.370 NA uniform ladder of mass mmm and length lll leans at an angle θθtheta against a frictionless wall (Figure 1).If the coefficient of static friction between the ladder and the ground is μμmu, determine a formula for the minimum angle at which the ladder will not slip. Express your answer in terms of some or all of the variables mmm, lll, and μμmu.