A small metal ball with a mass of m = 80.1 g is attached to a string of length I = 1.25 m. It is held at an angle of 0 = 56.5° with respect to the vertical. The ball is then released. When the rope is vertical, the ball collides head-on and perfectly elastically with an identical ball originally at rest. This second ball flies off with a horizontal initial velocity from a height of h = 2.94 m, and then later it hits the ground. At what distance x will the ball land?
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- You hold a slingshot at arms length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 200 cm/s. With the same procedure, you fire a bean with speed 600 cm/s. What is the ratio of the mass of the bean to the mass of the pebble? (a) 19 (b) 13 (c) 1 (d) 3 (e) 9A 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?A block of mass m1 = 4.00 kg initially at rest on top of a frictionless, horizontal table is attached by a lightweight string to a second block of mass m2 = 3.00 kg hanging vertically from the edge of the table and a distance h = 0.450 m above the floor (Fig. P8.77). If the edge of the table is assumed to be frictionless, what is the speed with which the first block leaves the edge of the table?
- A 61.5-kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.4 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 9.4 m/s as y = 0. What is her kinetic energy at this point? What is the gravitational potential energy associated with the athlete? (c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete? (d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. (e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/sA pendulum consists of a 2 kg bob attached to a light string of length 6.0 m. The bob is struck horizontally so that it has an initial horizontal velocity of 3.0 m/s. What is the angle of the string with the vertical when the bob reaches its maximum height?A 66.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.5 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 7.5 m/s as y = 0. What is her kinetic energy at this point? JWhat is the gravitational potential energy associated with the athlete? J(c) What is her kinetic energy at maximum height? JWhat is the gravitational potential energy associated with the athlete? J(d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m(e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/s
- A 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall. After the block collides with the spring, it keeps moving rightwards until the spring reaches its maximum compression of 1.68 m. After reaching maximum compression, the block and spring come to rest momentarily, and then move leftwards. While it is moving to the left, what is the speed of the block when it has moved so that the spring is compressed to only one-half of the maximum distance?A pendulum of length L = 1.0 meter and bob of mass m = 1.0 kg is released from rest at an angle θ = 30 degrees. When the pendulum reaches the vertical position, the bob strikes a cube with mass M = 3.0 kg that is resting on a frictionless table of height h = 0.85 m. d. Determine how far away from the bottom edge of the table, Δx, the cube will strike the floor e. At the location where the cube would have struck the floor, there is now a small cart of mass M = 3.0 kg and negligible height. The cube lands on the cart, and sticks to the cart in a completely *inelastic* collision. Ignore friction. Calculate the horizontal velocity of the cart just after the cube lands on it.In the figure, a ball of mass m = 56 g is shot with speed v₁ = 23 m/s (in the negative direction of an x axis) into the barrel of a spring gun of mass M = 223 g initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to friction between the ball and the barrel is negligible. (a) What is the speed of the spring gun after the ball stops in the barrel? (b) What fraction of the initial kinetic energy of the ball is stored in the spring? (a) Number i (b) Number Units Units M >
- Blocks A (mass 2.00 kg) and B (mass 6.00 kg) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 2.00 m/s. The blocks are equipped with ideal spring bumpers, . The collision is head-on, so all motion before and after the collision is along a straight line. (a) Find the maximum energy stored in the spring bumpers and the velocity of each block at that time. (b) Find the velocity of each block after they have moved apart.You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass mm is fired vertically upward into the bottom of the block. The spring's maximum compression dd is measured from its initial suspended position. Find an expression for the bullet's speed vB. Express your answer in terms of the variables mmm, M, k, d, and constant g What was the speed of a 15 gg bullet if the block's mass is 2.0 kg and if the spring, with k = 55 N/mN/m, was compressed by 47 ccm? Express your answer in meters per second to two significant figures.A mass M1 (of 2.5 kg) slides without friction on a table at a speed of 5 m/sec towards a mass M2 of 5 kg which can also slide without friction on the table. There is a spring on the face of M2 that will contact M1. If the spring constant is 100 N/m, what will be the maximum compression of the spring?