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
Want to see more full solutions like this?
Chapter 7 Solutions
Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term
- An inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?arrow_forwardAn inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P7.47. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest? Figure P7.47 Problems 47 and 48.arrow_forwardReview. This problem extends the reasoning of Problem 41 in Chapter 9. Two gliders are set in motion on an air track. Glider 1 has mass m1 = 0.240 kg and moves to the right with speed 0.740 m/s. It will have a rear-end collision with glider 2, of mass m2 = 0.360 kg, which initially moves to the right with speed 0.120 m/s. A light spring of force constant 45.0 N/m is attached to the back end of glider 2 as shown in Figure P9.41. When glider 1 touches the spring, superglue instantly and permanently makes it stick to its end of the spring. (a) Find the common speed the two gliders have when the spring is at maximum compression. (b) Find the maximum spring compression distance. The motion after the gliders become attached consists of a combination of (1) the constant-velocity motion of the center of mass of the two-glider system found in part (a) and (2) simple harmonic motion of the gliders relative to the center of mass. (c) Find the energy of the center-of-mass motion. (d) Find the energy of the oscillation.arrow_forward
- A giant swing at an amusement park consists of a 365-kg uniform arm 10.0 m long, with two seats of negligible mass connected at the lower end of the arm (Fig. P8.53). (a) How far from the upper end is the center of mass of the arm? (b) The gravitational potential energy of the arm is the same as if all its mass were concentrated at the center of mass. If the arm is raised through a 45.0 angle, find the gravitational potential energy, where the zero level is taken to be 10.0 m below the axis, (c) The arm drops from rest from the position described in part (b). Find the gravitational potential energy of the system when it reaches the vertical orientation. (d) Find the speed of the seats at the bottom of the swing.arrow_forwardTo form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.62 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same?arrow_forwardAn inclined plane of angle θ = 20.0° has a spring of force constant k = 495 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in the figure below. A block of mass m = 2.49 kg is placed on the plane at a distance d = 0.327 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?arrow_forward
- To measure the static friction coefficient between a 1.40-kg block and a vertical wall, a spring (k = 770 N/m) is attached to the block, is pushed on the end in a direction perpendicular to the wall until the block does not slip downward (see figure). If the spring is compressed by 0.048 m, what is the coefficient of static friction?arrow_forwardTwo rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m. Initially, the spring is unstretched and the bodies are at rest. If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then -20 Nm of work was done by the spring on the body A, B system. Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m. Initially, the spring is unstretched and the bodies are at rest. If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then -20 Nm of work was done by the spring on the body A, B system. True Falsearrow_forwardSuppose that a simple pendulum consists of a small 60.0 g bob at the end of a cord of negligible mass. If the angle u between the cord and the vertical is given by u = (0.0800 rad) cos[(4.43 rad/s)t + f], what are (a) the pendulum’s length and (b) its maximum kinetic energy?arrow_forward
- A spring oriented vertically is attached to a hard horizontal surface as in the figure below. The spring has a force constant of 1.32 kN/m. How much is the spring compressed when a object of mass m = 2.15 kg is placed on top of the spring and the system is at rest?arrow_forwardthe potential energy of a particle is given by U(x)= (9 J/m^4)x^4-(8 J/m^2)x^2. At what value of x would the particle be in unstable equilibrium? A.) -2/3 m B.) sqrt of 8/9 m c.) 0 m d.) 2/3 m e.) sqrt of - 8/9 marrow_forwardA spring with a constant of 300 N/m is stretched 1.5 m. What is the force in the spring? 100 N 50 N 300 N 150 N 450 N 200 Narrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning