8) A pendulum consists of a bob with mass m, attached to a string of length L. A block of mass M, rests on a horizontal frictionless surface. The pendulum is released from rest at an angle a with the vertical and bob collides elastically with the block. Following collision, the maximum angle of the pendulum with the vertical is measured as ß. Determine M in terms of g, a, ß and m.

8) A pendulum consists of a bob with mass m, attached to a string of length L. A block of mass M, rests on a horizontal frictionless surface. The pendulum is released from rest at an angle a with the vertical and bob collides elastically with the block. Following collision, the maximum angle of the pendulum with the vertical is measured as ß. Determine M in terms of g, a, ß and m.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter11: Collisions

Section: Chapter Questions

Problem 43PQ: Pendulum bob 1 has mass m1. It is displaced to height h1 and released. Pendulum bob 1 elastically...

See similar textbooks

Similar questions

Pendulum bob 1 has mass m1. It is displaced to height h1 and released. Pendulum bob 1 elastically collides with pendulum bob 2 of mass m2 (Fig. P11.43). FIGURE P11.43 a. Find an expression for the maximum height h2 of pendulum bob 2. b. If m2 = 2.5m1 and h1 = 5.46 m, what is h2?
There is a compressed spring between two laboratory carts of masses m1 = 105 g and m2 = 212 g. Initially, the carts are held at rest on a horizontal track (Fig. P10.40A). The carts are released, and the cart of mass m1 has velocity vi=2.035i m/s in the positive x direction (Fig. 10.40B). Assume rolling friction is negligible. a. What is the net external force on the two-cart system? b. Find the velocity of cart 2. FIGURE P10.40 Problems 40 and 41.
There is a compressed spring between two laboratory carts of masses m1 and m2. Initially, the carts are held at rest on a horizontal track (Fig. P10.40A). The carts are released, and the cart of mass m1 has velocity v1 in the positive x direction (Fig. P10.40B). Assume rolling friction is negligible. a. What is the net external force on the two-cart spring system? b. Find an expression for the velocity of cart 2. c. Sometimes, mistakes are made in a laboratory. For example, what changes in parts (a) and (b) if the track is not level as shown in Figure P10.40C? Explain your answer.
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretchcd and with force constant k = 2.00 104 N/m, as shown in Figure P8.60. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed 45.0 above the horizontal. (a) Assuming that the mass of the cannon and its carriage is 5 000 kg, find the recoil speed of the cannon. (b) Determine the maximum extension of the spring. (c) Find the maximum force the spring exerts on the carriage. (d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?
An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kinetic energy?
Two identical particles, each of mass 1 000 kg, are coasting in free space along the same path, one in front of the other by 20.0 m. At the instant their separation distance has this value, each particle has precisely the same velocity of 800 m/s. What are their precise velocities when they are 2.00 m apart? Figure P13 74
In Section 1.4, we considered the collision of a karate expert’s hand with a concrete block. Based on the graphs in Figure 1.31, the initial downward speed of the fist with mass 0.75 kg is about -13 m/s and the collision time is approximately 25 ms. Find the impulse and the average force exerted on the block by the fist during the collision.
A ball of mass 250 g is thrown with an initial velocity of 25 m/s at an angle of 30 with the horizontal direction. Ignore air resistance. What is the momentum of the ball after 0.2 s? (Do this problem by finding the components of the momentum first, and then constructing the magnitude and direction of the momentum vector from the components.)
Review. A 60.0-kg person running at an initial speed of 4.00 m/s jumps onto a 120-kg cart initially at rest (Fig. P9.37). The person slides on the carts top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.400. Friction between the cart and ground can be ignored. (a) Find the final velocity of the person and cart relative to the ground. (b) Find the friction force acting on the person while he is sliding across the top surface of the cart. (c) How long does the friction force act on the person? (d) Find the change in momentum of the person and the change in momentum of the cart. (c) Determine the displacement of the person relative to the ground while he is sliding on the cart. (f) Determine the displacement of the cart relative to the ground while the person is sliding. (g) Find the change in kinetic energy of the person. (h) Find the change in kinetic energy of the cart. (i) Explain why the answers to (g) and (h) differ. (What kind of collision is this one, and what accounts for the loss of mechanical energy) Figure P9.37
(a) Figure P9.36 shows three points in the operation of the ballistic pendulum discussed in Example 9.6 (and shown in Fig. 9.10b). The projectile approaches the pendulum in Figure P9.36a. Figure P9.36b shows the situation just after the projectile is captured in the pendulum. In Figure P9.36c, the pendulum arm has swung upward and come to rest momentarily at a height A above its initial position. Prove that the ratio of the kinetic energy of the projectilependulum system immediately after the collision to the kinetic energy immediately before is m1|/(m1 + m2). (b) What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before? (c) A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth? Figure P9.36 Problem. 36 and 43. (a) A metal ball moves toward the pendulum. (b) The ball is captured by the pendulum. (c) The ballpendulum combination swings up through a height h before coming to rest.
A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?
A particle is suspended from a post on top of a can by a light string of length L. as shown in Figure P9.57a. The can and particle are initially moving to the right at constant speed the with the string vertical. The can suddenly comes to rest when it runs into and sticks to a bumper as shown in Figure P9.57b. The suspended panicle swings through an angle . (a) Show that the original speed of the cart can be computed from. vi=2gL(1cos) (b) If the bumper is still exerting a horizontal force on the cart when the hanging panicle is at its maximum angle forward from the vertical. at what moment does the bumper stop exerting a horizontal force?