1.7Tutorial ExerciseTo test the resiliency of its bumper during low-speed collisions, a 1 655-kg automobile is driven into a brick wall.The car's bumper behaves like a spring with a force constant 7.00 x 106 N/m and compresses 3.29 cm as the caris brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed ortransferred away during impact with the wall?Part 1 of 3 - ConceptualizeIf the bumper is only compressed a few cm, the car is probably not permanently damaged, so v is probably lessthan about 5 m/s.Part 2 of 3 - CategorizeAssuming no mechanical energy turns into internal energy during impact with the wall, the initial energy (kinetic)equals the final energy (elastic potential).Part 3 of 3 - AnalyzeWe choose the car with its shock-absorbing bumper as the system. By conservation of energy, we haveK₁ = U₁ or mv² = ¹kx².Solving for the velocity,x 10-2 mm/s.Submit Skip (you cannot come back)x 106 N/mkg

Answered: Image /qna-images/answer/896b55aa-2e04-4905-941d-2455f5f3b9b4.jpg

To test the resiliency of its bumper during low-speed collisions, a 1 655-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 7.00 x 106 N/m and compresses 3.29 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall?

To test the resiliency of its bumper during low-speed collisions, a 1 655-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 7.00 x 106 N/m and compresses 3.29 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall?

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 toy cannon uses a spring to project a 5.28 -g soft rubber ball. The spr a force constant of 8.04…

Q: P 00000

A: Given: Mass. m = 10kg Force constant, k = 0.80kN/m Force, P = 80N

Q: A 1.42-kg box rests atop a massless vertical spring with k = 3960 N/m that has been compressed by…

A: Given data: Mass (m) = 1.42 kg Spring constant (k) = 3960 N/m Comparison in spring (x) = 13.5 cm =…

Q: A 2.4 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it…

A: Using energy conservation KE=PE stored in spring

Q: The horizontal surface on which the block (mass m=2 kg) slides is frictionless. The speed of the…

Q: In preparation for shooting a ball in a pinball machine, a spring (k = 713 N/m) is compressed by…

Q: Iace with d speed of 1.8 m/s when it encounters a spring. (a) Determine the force constant (in N/m)…

A: Mass "m" = 2.6 kg . initial velocity "u" = 1.8m/s .

Q: A spring with constant 56 N/m is positioned so that is sits right below an object of mass 5.0 kg.…

Q: a box of mass m = 9.20 kg is sliding across a horizontal frictionless surface with an initial speed…

A: According to the law of conservation of energy , energy can neither be created nor destroyed but can…

Q: A 1.2 kg block is held at rest against a spring with a force constant k = 750 N/m. Initially, the…

Q: 22. A 5.00×10^5 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large…

A: The potential energy stored in spring is given by Where k = force constant of the spring, x =…

Q: A toy cannon uses a spring to project a 5.28-g soft rubber ball. The spring is originally compressed…

A: mass = 5.28 g original compression (d) = 4.90 cm k = 8.01 N/m d1 = 15.9 cm f = 0.0323 N

Q: A toy cannon uses a spring to project a 5.21-g soft rubber ball. The spring is originally compressed…

Q: An 8.0 g bullet is shot into a 3.0 kg block, at rest on a frictionless horizontal surface. The…

A: The compression in the spring x=3.3 cm=3.3×10-2 m The spring constant k=2700 N/m The energy stored…

Q: A 45 kg gymnast is bouncing on a trampoline. Model the gymnast as a particle and the trampoline as a…

A: given that,k=15000 NmA=30cm=0.3 mm=45 kgg=9.8ms2

Q: A 6.00 ✕ 105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large…

Q: In the diagram below, a 63 kg rod has a box hanging from it and is suspended from the ceiling by a…

A: Given, The mass of rod will be mR=63 Kg Length of A in statice equilibrium, A=14 cm Length of B in…

Q: If a 4-kg block is placed against the spring and the spring is released, what will be the speed of…

A: GIVEN: Mass of block =4 kg For the spring Work done =12kx2 where k is spring constant x…

Q: As shown in the figure below, a box of mass m = 6.00 kg is sliding across a horizontal frictionless…

A: mass , m = 6 kg Initial speed , Vi = 3.2 m/s Spring constant , k = 2800 N/m To find = Spring…

Q: As shown in the figure below, a box of mass m = 9.80 kg is sliding across a horizontal frictionless…

A: given data as per question mass of box m = 9.8kg initial velocity v = 3.70m/s

Q: what was the initinal speed of the block?

Q: A 0.300-kg block along a horizontal track has a speed of 1.60 m/s immediately before colliding with…

Q: :) A spring with a constant k = 100 N/m is placed after point-C in the frictionless ABC path. A ball…

Q: 64 ing on a horizontal, frictionless table. The block is pushed 5- o the spring, compressing it by…

Q: As shown in the figure, a 1.50 kg box is held at rest against a spring with a force constant k = 725…

A: As per our honor code, we are allowed to answer only three subparts at a time, since it is not…

Q: A 2.0 kg ball is launched by means of a vertically oriented spring with spring constant k = 16.0…

Q: A toy cannon uses a spring to project a 5.35-g soft rubber ball. The spring is originally compressed…

Q: You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet…

A: From conservation of momentum is, mBvB=mB+Mvf ......(i) From conservation of energy,…

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

1.7
Tutorial Exercise
To test the resiliency of its bumper during low-speed collisions, a 1 655-kg automobile is driven into a brick wall.
The car's bumper behaves like a spring with a force constant 7.00 x 106 N/m and compresses 3.29 cm as the car
is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or
transferred away during impact with the wall?
Part 1 of 3 - Conceptualize
If the bumper is only compressed a few cm, the car is probably not permanently damaged, so v is probably less
than about 5 m/s.
Part 2 of 3 - Categorize
Assuming no mechanical energy turns into internal energy during impact with the wall, the initial energy (kinetic)
equals the final energy (elastic potential).
Part 3 of 3 - Analyze
We choose the car with its shock-absorbing bumper as the system. By conservation of energy, we have
K₁ = U₁ or mv² = ¹kx².
Solving for the velocity,
x 10-2 m
m/s.
Submit Skip (you cannot come back)
x 106 N/m
kg

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Use law of conservation of energy to find speed of car

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 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

A 5.00 ✕ 105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.500 m by a large spring bumper at the end of its track. What is the force constant k of the spring (in N/m)? (Enter a number.)N/m i tried 5.00 x 10^5 and i don't think it was correct..
A block with a mass of 30.0 kilograms (kg) is held against a spring with a force constant of k = 1.25×105 N/m. The spring is initially compressed 17.5 centimeters (cm) from equilibrium. Then the block is released, setting it into motion. The block initially slides along a frictionless surface, but then it encounters a 1.50 meter long rough patch where the coefficient of kinetic friction is 0.134. It then slides down a frictionless ramp, which is tilted at an angle of 19.5 degrees and has a length of 2.50 meters. How fast is the block moving when it reaches the bottom of the ramp? Give your answer in meters per second (m/s). Hint: use WNC = ΔK + ΔU.
As shown in the figure, a 1.50-kg box is held at rest against a spring with a force constant k = 790 N/m that is compressed a distance d. When the box is released, it slides across a surface that is frictionless, except for a rough patch that has a coefficient of kinetic friction u, = 0.400 and is 6.00 cm in length. If the speed of the box is 1.50 m/s after sliding across the rough patch, determine the initial compression d of the spring. cm Equilibrium position v=0' rough patch wwwwwn 6.00 cm
A 3.00 kg box that is sliding on frictionless surface with a speed of 15 m/s approaches a horizontal spring. The spring has a spring constant of 1900 N/m. m 10000000 How far will the spring be compressed in stopping the box? Submit Answer Tries 0/10 How far will the spring be compressed when the box's speed is reduced to half of its initial speed? Note: This is not saying that the box starts with half of the original speed, the box still starts with 15 m/s, the question asks how far the spring will have been compressed when it has slowed the box to half of that speed. Submit Answer Tries 0/10
A 2.00kg block is pushed against a spring with negligible mass and force constant k = 435 N/m , compressing it 0.215 m. When the block is released, it moves along a frictionless, horizontal surface. Find its velocity after the release?
A toy cannon uses a spring to project a 5.31-g soft rubber ball. The spring is originally compressed by 5.08 cm and has a force constant of 7.95 N/m. When the cannon is fired, the ball moves 14.0 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.031 2 N on the ball. (a) With what speed does the projectile leave the barrel of the cannon? m/s (b) At what point does the ball have maximum speed? cm (from its original position) (c) What is this maximum speed? m/s Need Help? Submit Answer Read It Watch It
A 3.0 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring. (a) Determine the force constant (in N/m) of the spring, if the box compresses the spring 4.7 cm before coming to rest. N/m (b) Determine the initial speed (in m/s) the box would need in order to compress the spring by 1.5 cm. m/s Additional Materials O Reading
You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1100 kg car moving at 0.60 m/s is to compress the spring no more than 7.3×10−2 m before stopping. What should be the force constant of the spring? Assume that the spring has negligible mass
A block of mass m = 2.00 kg is attached to a spring of force constant k = 440 N/m as shown in the figure below. The block is pulled to a position x:= 5.70 cm to the right of equilibrium and released from rest. x=0 x = x; (a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless. m/s (b) Find the speed the block has as it passes through equilibrium (for the first time) if the coefficient of friction between block and surface is μ = 0.350. m/s
A horizontal spring with stiffness 0.8 N/m has a relaxed length of 16 cm (0.16 m). A mass of 22 grams (0.022 kg) is attached and you stretch the spring to a total length of 29 cm (0.29 m). The mass is then released from rest. What is the speed of the mass at the moment when the spring returns to its relaxed length of 16 cm (0.16 m)? m/s