You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block and stops in the block. The spring's maximum compression d is measured. Find an expression for the bulletť's speed vg in terms of m, M, k, and d. What was the speed of a 10 g bullet if the block's mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 45 cm?

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block and stops in the block. The spring's maximum compression d is measured. Find an expression for the bulletť's speed vg in terms of m, M, k, and d. What was the speed of a 10 g bullet if the block's mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 45 cm?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A baseball ball has a mass of 0.142kg. The ball was dropped from a distance of one meter above the…

A: Since you have posted a question with a multiple sub parts, we will solve first three sub - parts…

Q: A 14.0-g bullet is fired into a block of wood with speed, = 270 m/s (see the figure below). The…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

Q: 3. You wake up one morning to find yourself in a strange room with opaque walls, and no visible…

A: Given data: Initial velocity (Vi) = 0 m/s Mass (m) = 75.8 kg Height (h) = 1.10 m Time (t) = 0.331 s…

Q: A cart of mass 4 kg is on frictionless surface and compressed against an ideal spring with spring…

A: Given data, Mass m1=4 kg Mass m2=8 kg Height h2=0.67 m Compression x=1.04 m Acceleration due to…

Q: 1. A 15-g bullet is shot vertically into an 2-kg block. The block lifts upward 8.0 mm (see the…

A: Mass of bullet= 15 g = 0.015 kg Mass of block= 2 kg The block lifts upward h = 8 mm = 8×10-3 m

Q: Measuring the speed of a bullet. A bullet of mass m is firedhorizontally into a wooden block of mass…

A: The kinetic friction force when the block and the embedded bullet slides as distance is,

Q: Suppose a 10.0g bullet is fired at speed 120m/s and embeds into a 1530g block of wood that is at the…

A: Given: Mass of the bullet m =10 g = 0.01 kg Mass of the wooden block M = 1530 g…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Given data: Mass (m) = 77.9 kg Initial velocity (Vi) = 0 m/s Height (h) = 1.79 m Time (t) = 0.302 s…

Q: A 22-g bullet traveling 290 m/s penetrates a 2.0 kg block of wood and emerges going 150 m/s. If the…

Q: The diagram shows two identical particles (labeled 1 and 2) that are moving in the x-y plane. The…

A: We need to find the magnitude of the net angular momentum of the particles about the origin.

Q: 5. Albert is driving a 1,200kg car towards east at 40m/s (90mi/hr.) approaching a RED light. He…

A: Given data: The mass car 1 is m1=1200 kg. The mass car 2 is m2=800 kg. The velocity of car 1 is…

Q: A golf ball of mass m = 0.18 kg is dropped from a height h. It interacts with the floor for t = 0.11…

Q: In the figure, block 1 (mass 1.3 kg) is moving rightward at 9.1 m/s and block 2 (mass 4.5 kg) is…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Mass of the body (m) = 75.1 kg Height (h) = 1.38 m Time (t) = 0.424 sec

Q: Dizzy is speeding along at 35m / s as she approaches the level section of track near the loading…

A: Dizzy is speeding along at u=35 m/s. A braking system abruptly brings the M=335-kg car (rider mass…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: 1850 NExplanation:

Q: We have the following information: A volleyball ball has a mass of 0.26kg. The ball was dropped…

A: The potential energy is U = m g h The kinetic energy is K = 0.5 mv2 where, m is the mass, v is…

Q: A light spring of force constant 4.00 N/m is compressed by 8.00 cm and held between a 0.250 kg block…

Q: A block of mass m=17 kg starts moving 100 ms^-1 up a frictionless hill of height 5 m. It hits a…

Q: What was the speed of a 12 g bullet if the block's mass is 2.5 kg and if the spring, with k = 58…

A: Given data: The mass of the bullet is m =0.012 kg The mass of the block is M= 2.5 kg The spring…

Q: Block 1 with mass m slides from rest along a frictionless ramp from height h = 2.5 m and then…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

A: Given that: m=66.5 kgh=1.02 mu=0t=0.274 seca=?

Q: I am driving down the street at 23.4 mi/h and suddenly I see a squirrel. I slam on the brakes in…

A: Given that: Speed of car, u = 23.4 mi/h = 23.4 X 1.60 = 37.44 km/h= 10.4 m/s Time of decleration, t…

Q: We have the following information: A softball ball has a mass of 0.18kg. The ball was dropped from…

Q: sure the speed of a ked to design an unet as part of you. ew job in the military sector. You decide…

A: Solution: A. The bullet and vertical spring-mass system before and after the collision is shown…

Q: A ballistic pendulum consists of a 3.5-kg wooden block originally at rest, 0 = 0°. When a 2-g bullet…

Q: In the figure, block 1 (mass 3.2 kg) is moving rightward at 13 m/s and block 2 (mass 5.5 kg) is…

Q: One block of mass m_1=2.0 kg is sliding down along a frictionless ramp from a height of h=2.5 m. It…

Q: A cart of mass m₁ = 4 kg is on frictionless surface and compressed against an ideal spring with…

A: Let the velocity of first cart before hitting the second cart be v. Since this velocity is a result…

Q: You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors…

Q: The superheroine Xanaxa, who has a mass of 70.1 kg, is pursuing the 76.9 kg archvillain Lexlax. She…

Q: Problem Information: The A team is still falling in a tank and have 90 seconds before they reach the…

Q: Direction: Read and analyze the given problems. Solve each problem by showing your solution. Box the…

Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

100%

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose
spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of
mass m is fired vertically upward into the bottom of the block and stops in the block. The spring's
maximum compression d is measured. Find an expression for the bulletť's speed vg in terms of m, M, k,
and d. What was the speed of a 10 g bullet if the block's mass is 2.0 kg and if the spring, with k = 50 N/m,
was compressed by 45 cm?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Block A (with mass 10 kg) slides along a frictionless floor with a speed of 0.75 m/s and collides with Block B (with mass 12 kg) which was at rest and is attached to a spring with spring constant 24 N/m. The blocks stick together after the collision; what is the maximum compression of the spring?
A 31.0-kg skateboarder rides on a 10.0-kg skateboard at 5.7 m/s on a level road before jumping into air with a speed of 10.0 m/s against the ground in the direction of 27.0◦ above the forward, horizontal direction to leave the skateboard. Ignore air resistance and the friction between the road and skateboard. What is the maximum height that the skateboarder can reach? (A) 1.05 m; (B) 1.25 m; (C) 1.45 m; (D) 1.65 m; (E) 1.85 m. What is the speed of the skateboard on the ground after the jump? (A) 3.85 m/s; (B) 4.05 m/s; (C) 4.25 m/s; (D) 4.45 m/s; (E) 4.65 m/s. What is the minimum work done by the skateboarder to make the jump? (A) 994J; (B) 974J; (C) 954J; (D) 934J; (E) 914J.
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 50.1 kg. You pick up an object and drop it from rest, starting at a height of 1.97 meters above the floor, and it hits the floor 0.380 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 684 N 911 N 1,367 N 491.5 N
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 53.3 kg. You pick up an object and drop it from rest, starting at a height of 2.40 meters above the floor, and it hits the floor 0.560 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 544 N 816 N 522.9 N 408 N
A toy rocket operates by having a spring-loaded tube which ejects a small model rocket when released. The spring inside has a spring constant k = 625N/m, the rocket has a mass of 0.100 kg, and the maximum compression of the spring is 0.18 m. Consider the system of the rocket, spring, and the earth. Consider the interval of time between t1, when the rocket is released from the point of maximum spring compression, and t2, the moment when the spring is fully released and the rocket leaves the launcher. List below the types of energy that are changing during this interval and whether the changes are positive or negative. Please explain how you know.
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 56.0 kg. You pick up an object and drop it from rest, starting at a height of 2.35 meters above the floor, and it hits the floor 0.346 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 549.4 N 1,100 N 1,466 N 2,199 N
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 72.3 kg. You pick up an object and drop it from rest, starting at a height of 1.52 meters above the floor, and it hits the floor 0.223 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 1 2,210 N 2 2,947 N 3 4,420 N 4 709.3 N
When some cars are advertised, they quote a "stopping distance" from some speed to zero. The mass of the car and this value of "some speed" give a measure of initial motion, but we aren't necessarily told the mass. Using the stopping distance, one can directly calculate what physical quantity provided by the brakes? A impulse B chemical potential energy C power D kinetic energy E force F velocity G work H acceleration I mass
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 71.1 kg. You pick up an object and drop it from rest, starting at a height of 1.82 meters above the floor, and it hits the floor 0.305 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 1,391 N 1,855 N 2,782 N 697.5 N
Cons Block 1, of mass m1 = 2.90 kg , moves along a frictionless air track with speed vị with block 2, of mass m2 = 57.0 kg , which was initially at rest. The blocks stick together after the collision. (Figure 1) 13.0 m/s. It collides %3D Part A Part B Part C What the change AK = Kfinal – Kiniti. in the two-block system's kinetic energy due the collision? Express your answer numerically in joules. • View Available Hint(s) Figure 1 of 1 HV ΑΣφ ? Before collision: m2 m1 AK = 1 Submit After collision: Provide Feedback 1 2.
A 66.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.5 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? This answer has not been graded yet. (b) Select the height at which the athlete's speed is 7.5 m/s as y = 0. What is her kinetic energy at this point? JWhat is the gravitational potential energy associated with the athlete? J(c) What is her kinetic energy at maximum height? JWhat is the gravitational potential energy associated with the athlete? J(d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. m(e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer. m/s
You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 54.7 kg. You pick up an object and drop it from rest, starting at a height of 1.20 meters above the floor, and it hits the floor 0.396 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body?