15.0 kg wwwww 3.00 kg 8.00 m/s
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A 15.0 kg block is attached
to a very light horizontal spring of force constant 500.0 N/m and is resting
on a frictionless horizontal table (Fig.). Suddenly it is struck
by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon
the stone rebounds at 2.00 m>s horizontally to the left. Find the
maximum distance that the block will compress the spring after the
collision.
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- Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. (See (Figure 1).) The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20 g bullet into a 2.50 kg block hanging by a thin wire 75.0 cm long, causing the block to swing upward to a maximum angle of 32.6 ∘ from the vertical. What was the original speed of this bullet?Consider a frictionless track as shown in the figure below. A block of mass m, = 2.00 kg is released from point O from a height of h = 1.15 m. It makes a perfectly inelastic collision at point ® with a block of mass m, = 2.00 kg that is initially at rest. After the collision, the block of mass m, moves to the right and collides with a spring at point ©. The spring is attached to a wall and has a spring constant of 8.81 kN/m. A m h m2 B (a) Calculate the energy loss during the collision. Enter the magnitude. 4.0 (b) Calculate the maximum compression of the spring. 4.0 cm (c) Instead of an inelastic collision, consider a head-on elastic collision at point ®. During this specific elastic collision when the masses are equal, m, transfers its kinetic energy to m, and as a result, m, comes to rest. Calculate the maximum compression of the spring. 4.0 cmA 5.00-g bullet moving with an initial speed of vo = 360 m/s is fired into and passes through a 1.00-kg block, as in the figure below. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 885 N/m. Vo www 5.00 cm- (a) If the block moves 5.00 cm to the right after impact, find the speed at which the bullet emerges from the block. m/s (b) If the block moves 5.00 cm to the right after impact, find the mechanical energy lost in the collision.
- An 11,000-kg freight car rests against a spring bumper at the endof a railroad track. The spring has constant k = 0.32 MN/m. Thecar is hit by a second car of 9400-kg mass moving at 8.5 m/s, andthe two couple together. Find (a) the maximum compression ofthe spring and (b) the speed of the two cars when they reboundtogether from the spring.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?Both answer are wrong
- Two objects of masses m, - 0.54 kg and m, - 0.98 kg are placed on a horizontal frictionless surface and a compressed spring of force constant.20 m is placed between them as in figure (a). Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of 9.4 cm. If the objects are released from rest, find the final velocity of each object as shown in figure (b). (Let the positive direction be to the right. Indicate the direction with the sign of your answer.) m/s m/s V2 =Problem 4. A 15.0-kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table (see figure below). Suddenly it is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right. The collision is totally inelastic. (a) Find the velocity of the stone-block just after collision. (b) Find the maximum distance that the stone-block will compress the spring after the collision. 15.0 kg 3.00 kg 8.00 m/sA 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?
- In the ballistic pendulum experiment, a bullet of mass 0.06 kg is fired horizontally into a wooden block of mass 0.2 kg. The wooden block is suspended from the ceiling by a long string. The collision is perfectly inelastic and after impact the bullet and block swing together until the block is 0.12 m above its initial position. Find the velocity of the bullet and block just after impact. Answer in m/s.A block of mass M = 5.50 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6030 N/m. A bullet of mass m - 8.90 g and velocity of magnitude 740 m/s strikes and is embedded in the block (the figure). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion. (a) Number i (b) Number i Units Units m M k 000000000An object of mass 3.0 kg is held in placespring with spring constant k = 185 N/mrests on a horizontal plane surfacewithout turning on. The other end of the springconnected to the wall. Another thinga mass of 1.6 kg is thrown towards a mass of 3.0kg and pound it with an elastic impactperfect. Maximum spring compression is 80cm. Determine the speed of the incoming mass (mass1.6kg).