A 20 kg child is on a swing that hangs from 2.8-m-long chains. You may want to review (Pages 234 - 238). Part A For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Car rolling down a hill. What is her maximum speed if she swings out to a 44 ° angle? Express MOU

A 20 kg child is on a swing that hangs from 2.8-m-long chains. You may want to review (Pages 234 - 238). Part A For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Car rolling down a hill. What is her maximum speed if she swings out to a 44 ° angle? Express MOU

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter6: Applications Of Newton's Laws

Section: Chapter Questions

Problem 25P: Solving Problems with Newton’s Laws A 30.0-kg girl in a swing is pushed to one side and held at rest...

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You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in Figure P7.41. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2 = 3 400 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with the first to increase the force to the left on the car in Figure P7.41. When the spring with spring constant k2 compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can no longer compress. A typical car on the siding has a mass of 6 000 kg. When you present your design to your supervisor, he asks you for the maximum speed that a car can have and be stopped by your device. Figure P7.41
A child jumps tip and down on a bed, reaching a higher height after each bounce. Explain how the child can increase his maximum gravitational potential energy with each bounce.
A 75.0-kg firefighter slides down a pole while a constant friction force of 300 N retards her motion. A horizontal 20.0-kg platform is supported by a spring at the bottom of the pole to cushion the fall. The firefighter starts from rest 4.00 m above the platform, and the spring constant is 4 000 N/m. Find (a) the firefighters speed just before she collides with the platform and (b) the maximum distance the spring is compressed. Assume the friction force acts during the entire motion.
Unreasonable Results A mother pushes her child on a swing so that his speed is 9.00 m/s at the lowest point of his path. The swing is suspended 2.00 m above the child's center of mass. (a) What is the magnitude of the centripetal acceleration of the child at the low point? (b) What is the magnitude of the force the child exerts on the seat if his mass is 18.0 kg? (c) What is unreasonable about these results? (d) Which premises are unreasonable or inconsistent?
Figure CQ15.5 shows graphs of the potential energy of four different systems versus the position of a particle in each system. Each particle is set into motion with a push at an arbitrarily chosen location. Describe its subsequent motion in each case (a), (b). (c). and (d).
In a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patients body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 375 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.60 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.20 N on it. Find (a) the maximum speed of the needle and (b) the speed at which a flange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm.
A block is connected to a spring that is suspended from the ceiling. Assuming air resistance is ignored, describe the energy transformations that occur within the system consisting of the block, the Earth, and the spring when the block is set into vertical motion.
Solving Problems with Newton’s Laws A 30.0-kg girl in a swing is pushed to one side and held at rest by a horizontal force Fso that the swing ropes are 30.0with respect to the vertical. (a) Calculate the tension in each of the two ropes supporting the swing under these conditions. (b) Calculate the magnitude of F .
Does the kinetic energy of an object depend on the frame of reference in which its motion is measured? Provide an example to prove this point.
A sprinter of mass m accelerates uniformly from rest to velocity v in t seconds. (a) Write a symbolic expression for the instantaneous mechanical power P required by the sprinter in terms of force F and velocity v. (b) Use Newtons second law and a kinematic equation for the velocity at any time to obtain an expression for the instantaneous power in terms of m, a, and t only. (c) If a 75.0-kg sprinter reaches a speed of 11.0 m/s in 5.00 s, calculate the sprinters acceleration, assuming it to be constant. (d) Calculate the 75.0-kg sprinters instantaneous mechanical power as a function of time t and (e) give the maximum rate at which he burns Calories during the sprint, assuming 25% efficiency of conversion form food energy to mechanical energy.
An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box? Explain.
A pendulum, comprising a light string of length L and a small sphere, swings in the vertical plane. The string hits a peg located a distance d below the point of suspension (Fig. P8.40). (a) Show that if the sphere is released from a height below that of the peg, it will return to this height after the string strikes the peg. (b) Show that if the pendulum is released from rest at the horizontal position ( = 90) and is to swing in a complete circle centered on the peg, the minimum value of d must be 3L/5. Figure P8.40