A wooden block of mass M, attached to a massless spring with spring constant k, rests on its equilibrium position on a frictionless floor. A silver dart with mass m and velocity v is shot into the block and sticks to it. What is the maximum compression of the spring? m k m+M Ak (m + M)v √mk mv (m + M)k
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- There is a compressed spring between two laboratory carts of masses m1 and m2. 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 v1 in the positive x direction (Fig. P10.40B). Assume rolling friction is negligible. a. What is the net external force on the two-cart spring system? b. Find an expression for the velocity of cart 2. c. Sometimes, mistakes are made in a laboratory. For example, what changes in parts (a) and (b) if the track is not level as shown in Figure P10.40C? Explain your answer.A wooden block of mass M, attached to a massless spring with spring constant k, rests on its equilibrium position on a frictionless floor. A silver dart with mass m and velocity v is shot into the block and sticks to it. What is the maximum compression of the spring? mu O √(m + M)k O m+M k ○ (m + M)v √mk m kthe massless spring of a spring gun has a force constant k= .04N/cm. When the gun is aimed vertically, a 25g projectile is shot to a height of 5m above the end of the expanded spring. How much was the spring compressed initially?
- A 14.0-g bullet is fired into a block of wood with speed, = 270 m/s (see the figure below). The block is attached to a spring that has a spring constant of 200 N/m. The block with the embedded bullet compresses the spring a distance d = 32.0 cm to the right, before momentarily coming to a stop. V m eeeeeee d Determine the mass of the wooden block. (Express your answer to two significant figures.) kg27. A bullet with mass m, is fired with a velocity v; to a hanging target made of wood with mass m, and got stuck inside it but is able to bring the wood target at a height h. Derive an expression for the final velocity of the bullet.An object with mass m, = 2m which moves on horizontal surface with constant speed v, collides with an object with mass m2 = 3m, which was initially at rest. After the collision the two objects stick together and continue to move until they compress a spring with force constant k. What is the speed of the compound object with mass (m1 + m2), when the spring is compressed by a distance r? 2mv² 5k а. kr² 5m Ob. 4mv? 3k C. 5 O d. 4v2 V 25 kz2 е. kx²
- A block of mass 3.63 Kg slides on a frictionless horizontal tablet at a speed of 1.22 m/s. It comes to rest when it is in its path and compresses a spring whose force constant is 135 N/m. How much the spring is compressed???In your job in a police lab, you must design an apparatus to measure the muzzle velocities of bullets fired from handguns. Your solution is to attach a 2.00 kgkg wood block that rests on a horizontal surface to a light horizontal spring. The other end of the spring is attached to a wall. Initially the spring is at its equilibrium length. A bullet is fired horizontally into the block and remains embedded in it. After the bullet strikes the block, the block compresses the spring a maximum distance dd. You have measured that the coefficient of kinetic friction between the block and the horizontal surface is 0.38. The table below lists some firearms that you will test. A grain is a unit of mass equal to 64.80 mgmg. Bullet ID Type Bullet Mass(grains) Muzzle Velocity(ft/sft/s) A .38Spec Glaser Blue 80 1667 B .38 Spec Federal 125 945 C .44Spec Remington 240 851 D .44Spec Winchester 200 819 E .45ACP Glaser Blue 140 1355 a)You want the maximum compression of the spring to be…In your job in a police lab, you must design an apparatus to measure the muzzle velocities of bullets fired from handguns. Your solution is to attach a 2.00 kgkg wood block that rests on a horizontal surface to a light horizontal spring. The other end of the spring is attached to a wall. Initially the spring is at its equilibrium length. A bullet is fired horizontally into the block and remains embedded in it. After the bullet strikes the block, the block compresses the spring a maximum distance dd. You have measured that the coefficient of kinetic friction between the block and the horizontal surface is 0.38. The table below lists some firearms that you will test. A grain is a unit of mass equal to 64.80 mgmg. Bullet ID Type Bullet Mass(grains) Muzzle Velocity(ft/sft/s) A .38Spec Glaser Blue 80 1667 B .38 Spec Federal 125 945 C .44Spec Remington 240 851 D .44Spec Winchester 200 819 E .45ACP Glaser Blue 140 1355 a)Of bullets AA through EE, which will produce the maximum…
- 4. A block of mass m is on a frictionless track, initially at a height h above the ground. The block slides down the track and collides at the bottom with a larger block of mass 3m. The two blocks stick together and move off to the right. Finally they are brought momentarily to rest by a spring with spring constant k. Fnd the maximum amount by which the spring will be compressed in stopping the combined blocks. [Ans: d = mgh/(2k)] h 3m Problem 4 Problem 5 EA block having a mass of 1.0 kg is given an initial velocity v= 6 m/s to the right and collides with a spring whose mass is negligible and whose force constant is k =100 N/m . Assuming the surface to be frictionless, e the maximum compression of the spring after the collision m 6 m 5 m NoneA cart of mass m₁ = 4 kg is on frictionless surface and compressed against an ideal spring with spring constant k = 158 N/m for a distance of x = 1.08 m. After it is released, it hits a second cart of mass m₂ = 9 kg and bounces back while the second car continues traveling onto a ramp where it reaches a height of h₂ = 0.69 m. Find the magnitude of the velocity of the first cart in m/s immediately after hitting the second cart. Use g = 9.8 m/s² and retain your answer to two decimal places. k m1 m2 Im m1 Loo! m2 I h₂