Two gliders are set in motion on an air track. A light spring of force constant k is attached to the back end of the second glider. As shown in the figure below, the first glider, of mass m₁, moves to the right with a speed V₁, and the second glider, of mass m₂, moves more slowly to the rightwith a speed, V2.VIm2iWhen m₁ collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of V1, V2, m₁, m2, and k, find the following. (Use any variable or symbol stated above as necessary.)(a) speed v at maximum compressionV =(b) the maximum compression XmaxXmax =(c) the speed of each glider after m₁V1f =has lost contact with the spring (Use any variable or symbol stated above as necessary.)V2f

Step 1: Part (a).Step 2: Part (b).Step 3: Part (c).Step 4:

Answered: Two gliders are set in motion on an air…

University Physics Volume 1

18th Edition

ISBN:9781938168277

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

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

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 33P: A hockey puck of mass 150 g is sliding due east on a frictionless table with a speed of 10 m/s....

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Similar questions

A hockey puck of mass 150 g is sliding due east on a frictionless table with a speed of 10 m/s. Suddenly, a constant force of magnitude 5 N and direction due north is applied to the puck for 1.5 s. Find the north and east components of the momentum at the end of the 1.3-s interval.
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?
Can momentum be conserved for a system if there are external forces acting on the system? If so, under what conditions? If not, why not?
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) 9
Two figure skaters are coasting in the same direction, with the leading skater moving at 5.5 m/s and the trailing skating moving at 6.2 m/s. When the trailing skater catches up with the leading skater, he picks her up without applying any horizontal forces on his skates. If the trailing skater is 50 heavier than the 50-kg leading skater, what is their speed after he picks her up?
A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 3.0 m/s, what is the maximum mass of grain that it can accept?
The coefficient of friction between the block of mass ml = 3.00 kg and the surface in Figure P7.22 is k = 0.400. The system starts from rest. What is the speed of the ball of mass, m2 = 5.00 kg when it has fallen a distance h = 1.50 m? Figure P7.22
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.
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) 9
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?
Which has a larger magnitude of momentum: a 3000-kg elephant moving at 40 km/h or a 60-kg cheetah moving at 112 km/h?
Check Your Understanding Even if there were some friction on the ice, it is still possible to use conservation of momentum to solve this problem, but you would need to imposed an additional condition on the problem. What is that additional condition?

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