In the ballistic pendulum shown below, the block has a mass of 2.1 kg, the bullet has a mass of 0.0067 kg, and the string has a length of 2.21 m. A bullet is shot directly at the block, lodging into the block, and causing the pendulum to swing forward 21°. 0
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- Two objects of masses m1 = 0.56 kg m2 = 0.88 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k = 280 N/m is placed between them as in Figure P6.28a. Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of 9.8 cm. If the objects are released from rest, find the final velocity of each object as shown in Figure P6.28b. Figure P6.28A 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?The forces shown in theforce vs. time diagram inFigure P6.17 act on a 1.5 - kgparticle. Find (a) the impulsefor the interval from t = 0 tot = 3.0 s and (b) the impulsefor the interval from t = 0 tot = 5.0 s. If the forces act on a1.5 - kg particle that is initiallyat rest, find the particle’sspeed (c) at t = 3.0 s and(d) at t = 5.0 s.
- A 4.2 kg rifle shoots a 0.050 kg bullet at a velocity of 3.00 x 10^2 m/s. At what velocity does the rifle recoil? (An explanation would help , thank you :)!)A bullet, having a mass of 0.04 kg moving with a velocity of 450 m/s penetrates a distance of 0.08 m into a wooden block firmly attached to the earth. Assuming a constant accelerating force, compute the following: a) the acceleration of the bullet, b) the accelerating force, c) the time of acceleration, and d) the impulse of the collision.During a spacewalk, a 118 kg astronaut (including her spacesuit) is at rest and holding a 3.5 kg wrench. If she throws the wrench with speed 12 m/s, then what will be her recoil speed?
- A cannon is rigidly attached to a carriage, which can movealong horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k = 2.00 x 104 N/m, as inFigure P6.75. The cannon fires a 2.00 x 102-kg projectile at a velocity of 125 m/s directed 45.0° above the horizontal.(a) If the mass of the cannon and its carriage is 5.00 x 103-kg, find therecoil speed of the cannon. (b) Determine the maximum extensionof the spring. (c) Find the maximum force the spring exertson the carriage. (d) Consider the system consisting of the cannon,the carriage, and the shell. Is the momentum of this systemconserved during the firing? Why or why not?We have a ballistic pendulum with the force acting between the ball and pendulum during the ball's capture being very large. Why does this large force not affect the conservation of momentum during capture? Why can't we use conservation of momentum when the pendulum-ball system swings upward yet we can use the conservation of mechanical energy instead?USING THE UAM FORMULA, SOLVE: A constant force of 3.5 N acts on a 7 kg block, initially at rest, for 7.0 s. Find the(a) acceleration of the block, (b) speed of the block at the end of 7.0 s, (c) change in momentum of the block, and (d) impulse produced by the force.
- The force shown in theforce vs. time diagram inFigure P6.15 acts on a 1.5-kgobject. Find (a) the impulseof the force, (b) the finalvelocity of the object if it isinitially at rest, and (c) thefinal velocity of the objectif it is initially moving alongthe x - axis with a velocity of-2.0 m/s.A 10 kg projectile was launched at the horizontal ground at a velocity of 20 m/s, 10 degrees with respect to the horizontal. The projectile hit a 30 kg box on top of a table at O. 177 seconds. If the box developed a speed of 5.140 rn/s after impact, what is the speed of the projectile after the collision?provide fbdConsider a ballistic pendulum with mass 4 kg. A bullet with mass 0.005 kg hits it with a velocity of 830 m/s and getslodged inside the pendulum. How high would the pendulum go?