An air-track cart of mass m₁ = 0.14 kg is moving with a speed vo=1.3 m/s to the right when it collides with a cart of mass m₂ = 0.25 kg that is at rest. Each cart has a wad of putty on its bumper, and hence they stick together as a result of their collision Suppose the average contact force between the carts is F = 1.5 N during the collision. (a) What is the acceleration of cart 1? Give direction and magnitude. (b)
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- Two equal mass objects undergo a perfectly elastic collision. One object is moving with a velocity v and the other is initially at rest. The collision is not head-on (two dimensional). Show that the two objects move away from each other perpendicularly (the velocity vectors of the two objects after the collision make a right angle).A puck of mass miis moving along a frictionless table at speed viin the +x- direction when it is hit simultaneously by 2lumps of clay, each of mass m2. Both lumps are traveling at a speed of v2when they hit the puck. One is traveling in the -x-direction, while the other one is dropped from above the table in the -y-direction. The puck and lumps of clay stick together. What is the speed of the puck and clay after the collision? Express your answer in terms of mim2v1and v2only. HINT: Write down the initial momentum of the puck m1. In which direction(s) is momentum conserved(i.e. in which direction(s) is there no net external force? Keep in mind that the table can provide an external normal force).Add the momenta of the lump(s) of clay for which momentum is conserved to your initial momentum. At the end of the day, the puck and both lumps of clay stick together so the final momentum is pf=(m1+m2+m2)vf. Set the initial and final momenta equal to each other and solve forvf.A 6.75-kg bowling ball moving at 8.95 m/s collides with a 0.875-kg bowling pin, which is scattered at an angle of θ = 24.5° from the initial direction of the bowling ball, with a speed of 11.2 m/s. Calculate the magnitude of the final velocity, in meters per second, of the bowling ball.
- A cue ball traveling at 6.57 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30.0° with its original direction of travel. (a) Find the angle between the velocity vectors of the two balls after the collision. (b) Find the speed of each ball after the collision.In the figure, block 1 of mass m slides from rest along a frictionless ramp from height h-3.1 m and then collides with stationary block 2. which has mass m2 - 4m,. After the collision, block 2 slides into a region where the coefficient of kinetic friction is 0.5 and comes to a stop in distanced within that region. What is the value of distance dif the collision is (a) elastic and (b) completely inelastic? Frictionles (a) Number Unit (b) Number UnitA cart with mass 330 g moving on a frictionless linear air track at an initial speed of 1.8 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 1.1 m/s. (a) What is the mass of the second cart? (b) What is its speed after impact? (c) What is the speed of the two-cart center of mass?
- A 200,000 kg railroad car moving at 3.00 m/s couples up with (sticks together) with another 150,000 kg car at rest. What is the final speed of the two cars immediately after the collision?A car of mass m moving at a speed v_1 collides and couples with the back of a truck of mass 2m moving initially in the same direction as the car at a lower speed v_2. (a) What is the speed v_f of the two vehicles immediately after the collision? (b) What is the change in kinetic energy of the car–truck system in the collision?A railroad car of mass 2.56 x 104 kg is moving with a speed of 4.10 m/s. It collides and couples with three other coupled railroad cars, each of the same mass as the single car and moving in the same direction with an initial speed of 2.05 m/s. (a) What is the speed of the four cars after the collision? (Round your answer to at least two decimal places.) m/s (b) How much mechanical energy is lost in the collision?
- One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted by a 0.100 mg chip of paint that strikes a spacecraft window at a relative speed of 4.00 × 10³ m/s, given the collision lasts 6.00 x 10-8 s.As part of a carnival game, a m, = 0.528 kg ball is thrown at a stack of 24.8 cm tall, m, = 0.383 kg objects and hits with a perfectly horizontal velocity of v,i = 10.3 m/s. Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of vhf = 3.10 m/s in the same direction, the topmost object has an angular velocity of @, = 1.63 rad/s about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of the torque due to gravity during the collision is negligible. If the object's center of mass is located r = 17.4 cm below the point where the ball hits, what is the moment of inertia I, of the object about its center of mass? I, = kg-m? What is the center of mass velocity vo cm of the tall object immediately after it is struck? Vb.i Vo.cm = m/sA freight train is being assembled in a switching yard, with two boxcars. Car 1 has a mass of m1= 61x10^3 kg and moves at a velocity of Vo1= +1 m/s. Car 2, with a mass of m2= 92x10^3 kg and a velocity 0f Vo2= +1 m/s, overtakes car ! and couples to it. Neglecting friction, find the common velocity (m/s) of the cars after they become coupled. Express in 3 decimal places.