Concept explainers
(a)
Maximum speed of the needle.
(a)
Answer to Problem 83P
Maximum speed is
Explanation of Solution
Consider the needle is fired horizontally from a spring. Maximum speed occurs just after the needle leaves the spring, before entering the body.
Write the law of conservation of energy for this case.
Here
Write the equation for initial and final kinetic energy.
Here
Write down the equation for initial and elastic potential energy.
Here
Write the equation for work done by the spring
Here
As the initial velocity s zero,
As there is no penetration into the body, distance covered is zero. Then
As there is no extension,
Substitute these results in (I) and write for
Conclusion:
Substitute
Maximum speed is
(b)
Speed to limit the penetration to
(b)
Answer to Problem 83P
Speed should be
Explanation of Solution
The initial elastic potential energy is converted partially into internal energy in the organ and partially kinetic energy of the needle.
Write the energy conservation equation for this case.
Here
Write the equation for initial and final work done by the spring
Here,
As the initial velocity s zero
As there is no extension,
Substitute (II), (III), (VII), (VIII) and (IX) in (VI) and write for
Conclusion:
Substitute
Speed should be
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Chapter 7 Solutions
Principles of Physics: A Calculus-Based Text
- A stepladder of negligible weight is constructed as shown in Figure P10.73, with AC = BC = ℓ. A painter of mass m stands on the ladder a distance d from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately. Figure P10.73 Problems 73 and 74.arrow_forwardA uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot located a distance = 4.00 m from the left end exerts a normal force n2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right as in Figure P10.28. The goal is to find the womans position when the beam begins to tip. (a) What is the appropriate analysis model for the beam before it begins to tip? (b) Sketch a force diagram for the beam, labeling the gravitational and normal forces acting on the beam and placing the woman a distance x to the right of the first pivot, which is the origin. (c) Where is the woman when the normal force n1 is the greatest? (d) What is n1 when the beam is about to tip? (e) Use Equation 10.27 to find the value of n2 when the beam is about to tip. (f) Using the result of part (d) and Equation 10.28, with torques computed around the second pivot, find the womans position x when the beam is about to tip. (g) Check the answer to part (e) by computing torques around the first pivot point. Figure P10.28arrow_forwardA mountain biker tries to start pedalling in the mud. The total mass (80 kg, bike + biker) is distributed equally between the front and rear wheels. There is a loss of 10% of moment of force between pedal and the rear wheel. The diameter of wheels is 70 cm, and the static friction coefficient between tyre and the mud is 0.3. The pedal angle is 25° from the vertical and has a length of 20 cm. The force exerted by the cyclist is vertical. What is the maximal force that the biker can produce without skidding?Hint 1: ImageHint 2: the value of Mp, the moment around the pedals, is about 50 Nm.arrow_forward
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- In the figure, a ladder of length L = 11 m and mass m = 48 kg leans against a slick (frictionless) wall. The ladder's upper end is at height h = 8.3 m above the pavement on which the lower end rests (the pavement is not frictionless). The ladder's center of mass is L/3 from the lower end. A firefighter of mass M = 71 kg climbs the ladder. Let the coefficient of static friction us between the ladder and the pavement be 0.46. How far (in percent) up the ladder must the firefighter go to put the ladder on the verge of sliding? Frictionless System Fire- Fire-/ fighter fighter com Ladder Ladder com a/3 a/2-arrow_forwardKathrine lets go of a cube of mass of m = 5 kilograms on her physics demo device she created. Her cube goes down a super smooth slide surface that has a height vertical distance of h=85 cm. At the end of the slide, her cube crashes into and sticks to the lower end of a vertical pole that has a mass M=10.5 kg and length 1-2.00m. Right after the crash, the pole pivots about a hinge point near its upper end through an angle (theta) before it stops for a moment. See the image given below to visualize Katherines system. You are tasked with Figuring out the following three things The speed of her cube just before it hits the pole The angular speed of the pole just after the crash The angle (theta) through which the pole pivots a. b. C. 0 Kathrine and her devicearrow_forwardThe 77.0 kg painter in the figure below is using a large stepladder. The base of the ladder is 3.0 m wide, and the ladder is 7.0 m high. The painter is on a step that is 2.0 m above the floor. The horizontal bar of the ladder has a mass of 10.0 kg, and the entire ladder has a mass of 64.0 kg. Assume that the floor is frictionless. A В C 7.0 m 5.0 m 2.0 m 3.0 m (a) Find the force of tension in the horizontal bar and the normal forces that the floor exerts on the ladder. T = Number N Njeft = Number N Nright = Number (b) Find the action-reaction forces at the hinges A, B, and C. Enter each answer as the magnitude of the component of the hinge forces. Consider the positive r-direction to be rightwards and the positive y-direction to be upwards.arrow_forward
- A board sits in equilibrium. On the left end, there is a wire that supports the board from the ceiling, and to the right, there is a sawhorse that supports the board from the ground. The sawhorse is a distance d= 1/5l from the right edge of the board. There is a block with mass ms= 4.5kg that is a distance 3/4l from the right edge of the board. Finally the board has a mass mb= 11kg. e) What is the force of tension and normal force on the board?arrow_forwardSolve it?arrow_forwardThe uniform thin pole has a weight of 30 lb and a length of 26 ft. If it is placed against the smooth wall and on the rough floor in the position d = 10 ft, will it remain in this position when it is released? The coefficient of static friction is us = 0.3. B 26 ftarrow_forward
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