A 45 kg gymnast is bouncing on a trampoline. Model the gymnast as a particle and the trampoline as a spring with a spring constant of 15,000 N/m. The spring is compressed by 30 cm when the gymnast is at her lowest point. We want to determine how high she goes above the trampoline.

A 45 kg gymnast is bouncing on a trampoline. Model the gymnast as a particle and the trampoline as a spring with a spring constant of 15,000 N/m. The spring is compressed by 30 cm when the gymnast is at her lowest point. We want to determine how high she goes above the trampoline.

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: I find a spring that is labeled "80 N/m", but it is actually 3.5 inches long. I fasten a beam…

A: The length of the spring is given to be 3.5 inches. And it has been fastened from a beam 789mm above…

Q: A block of mass m = 3.25 kg slides along a horizontal table with speed up = 7.50 m/s. At x = 0, it…

A: Given data:The mass of the block is The initial speed of the mass The spring constant The…

Q: 50 N/m ell kg x = -0.3 m x= 0 m x= 0.3 m A block of mass 0.5 kg on a horizontal surface is attached…

Q: A 1.74 kg ball rolls on a frictionless horizontal surface at 5.67 m/s and collides with a stationary…

Q: - Xc + d 00004 m 3. Two identical springs of spring constant k are on opDosite sides of a flat table…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: A large toy car is pushed horizontally by a spring, and the spring has a spring constant of 135 N/m.…

Q: I have another solution using energy conservation where the gravitational potential energy is…

A: Solution: Given: m1 = mass of block 1 = 2.0 kg m2 = mass of block 2 = 3.0 kg X1 = extension in the…

Q: An 0.80-kg block is held in place against the spring by a 67-N horizontal external force (see the…

A: Given : Mass of a block (m) = 0.80 kg Horizontal external force (F) = 67 N Velocity (v1) = 1.2 m/s…

Q: A vertical spring with a spring constant of 490 N/m is mounted on the floor. From directly above the…

Q: A 2.5-kg block moving at 2.0 m/s collides with a spring whose spring constant is 3900 N/m, as shown…

Q: A 10 g bullet is shot into a 500 g block, at rest on a frictionless horizontal surface. The bullet…

A: Given data: The mass of the bullet is m = 10 g. The mass of the block is M = 500 g. The…

Q: A box is attached to a spring and at rest at the equilibrium position of the spring when a bullet…

A: When the body is placed at the surface with coefficient of friction μ, the friction force is given…

Q: A 25 kg child bounces on a pogo stick. The pogo stick has a spring with spring constant 2.0 x 104…

A: Given:Mass of the child (m) is 25 kg.Acceleration of child in upward direction ac is 9.8m/s2Spring…

Q: A 5.00×105-kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large…

A: Given: mass of subway, m = 5 × 105 kg initial speed, u = 5 m/s final speed, v = 0 stopping distance,…

Q: A spring with spring constant 26 N/m is compressed a distance of 8.5 cm by a ball with a mass of…

Q: simple pendulum is suspended from the ceiling by means of a string and the pendulum has a length of…

Q: A 9.20 kg rocket produces a thrust of 190 N. The rocket is pointed upward and the bottom of the…

A: Work done in stretching the spring will be,

Q: 61. A child's pogo stick (Fig. P8.61) stores energy in a spring with a force constant of 2.50 X 104…

A: Given: The force constant of the spring is k = 2.5 x 104 N/m The position of A is xA = - 0.1 m The…

Q: A vertical spring with a spring constant of 530 N/m is mounted on the floor. From directly above the…

Q: A 12.0 kg bowling ball (solid sphere) is rolling along a track at 2.7m/s. It then rolls up a ramp…

Q: wwwwww Ax A 0.8kg box on a horizontal frictionless surface is moving to the right at a speed of…

A: mass of box (m)=0.8 kgspeed of box (v)=2.19 m/smaximum compression in spring (∆x)=4 cm=0.04 m

Q: A 2.50-kg block is released from rest and allowed to slide down a frictionless surface and into a…

A: Given:Mass of the block = 2.5 kgInitial velocity of the block = oInitial height of the block = 0.500…

Q: 4. An 26 g rifle bullet traveling at 250 m/s buries itself in a 4.4 kg pendulum hanging on a 2.4 m…

A: mass of rifle bullet (m) = 26 g = 0.026 kg Speed of bullet (v) = 250 msMass of pendulum (M) = 4.4 kg…

Q: A spring-loaded toy gun is aimed vertically and fired after a spherical projectile of mass m =…

A: Given: The mass of the object is 28.5 kg. The sprign constant is 830 N/m. The compresson in the…

Q: A vertical spring with a spring constant of 490 N/m is mounted on the floor. From directly above the…

Q: A block of mass 1.5 kg is attached to a horizontal spring that has a force constant 800 N/m as shown…

A: The given data are listed below with appropriate variables. Here, m denotes the mass, k denotes the…

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

Q: A 2.5-kg block moving at 2. 0 m/s collides with a spring whose spring constant is 390 N/m, as shown…

A: a. according to the conservation of energy, for the given case, 12mvi2+mgh=12kΔx2

Q: A 5 kg block attached to a spring with a spring constant of 8 N/m oscillates horizontally on a…

A: Mass M =5kg Spring constant K= 8 N/m

Q: A child's toy consists of a piece of plastic attached to a spring in the figure below. The spring is…

A: The potential energy of the spring at maximum height is equal to the stored energy in the spring…

Q: A 6.00 kg block is permanently attached to a spring (k =500 N/m) on a rough ( 0.230,-0.210)…

Q: A block of mass m=7.3kg slides on a rough surface and moves toward a spring with a spring constant…

A: We have givenMass of block (m)=7.3 kgSpring constant (k) = 1659 N/mWhen Block is d=22.6 m away from…

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 child's toy consists of a piece of plastic attached to a spring in the figure below. The spring is…

A: According to the conservation of energy, 12kx2=mghkx2=2mghk=2mghx2

Q: A 0.87 kg block on a connected to a spring (whose spring constant is 3.80 N/m). The horizontal…

Q: A 25 kg child bounces on a pogo stick. The pogo stick has a spring with spring constant 2.0 x 104…

Q: A 2.0 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it…

A: a) Initial KE of box = m v^2 / 2 = (2×(1.8)^2 )/ 2 = 3.24 J Potential energy = (kx^2)/2…

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

A: NOTE: You have not mentioned the spring constant of the spring and the initial displacement of the…

Q: Rank each pendulum on the basis of the initial gravitational potential energy (before being…

Q: This relates the initial speed of the pendulum box to the height that it goes: V =sqrt 2 g h . The…

A: Given that, the speed can be expressed as, v=2gh

Q: Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two…

A: Given Mass m1 = 4 kg Mass m2 = 2 kg Spring constant k1 = 32 N/m…

Q: As shown in the figure, a 4.0-kg block is moving at 5.0 m/s along a horizontal frictionless surface…

Q: A block of mass m=5.5kg slides on a rough surface and moves toward a spring with a spring constant…

Q: OK, once again we have a pendulum, this time of length 1.92 m, which you release from rest at an…

A: Given data: Length of the pendulum, L=1.92 m θ1=58.3 ∘ θ2=11.7 ∘

Q: The bumper cars at the state fair have identical 1.0-m-long horizontal springs protruding from the…

A: The total kinetic energy is equal to the maximum potential energy. Apply the energy conservation…

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

How much work does gravity do on the gymnast as the moves 30 cm upward?
Express your answer with the appropriate units.
µA
W =
Value
Units

A 45 kg gymnast is bouncing on a trampoline.
Model the gymnast as a particle and the trampoline
as a spring with a spring constant of 15,000 N/m.
The spring is compressed by 30 cm when the
gymnast is at her lowest point. We want to
determine how high she goes above the
trampoline.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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 500-g block is released from rest and slides down a frictionless track that begins 1.90 m above the horizontal, as shown in the figure below. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a spring constant of 25.0 N/m. Find the maximum distance the spring is compressed.
You are showing your nieces how to make paper party decorations using paper springs. One niece makes a paper spring. The spring is stretched 8 cm and has a single sheet of colored paper suspended from it. You want the decorations to bounce at approximately 1 cy/s. How many sheets of colored paper should be used for the decoration on that spring if it is to bounce at 1 cy/s?
5:29 PM Sun Nov 5 Tt S An ideal spring is attached to the ceiling. While the spring is held at its relaxed length, a wooden block (M 850 g) is attached to the bottom of the spring, and a ball of clay (m 210g) is pressed onto the bottom of the block so that they stick together. The block+clay are gently lowered through a distance of d 2.7 cm and are then released, at which point they hang motionlessly from the bottom of the - spring. After a few minutes have passed, the clay unsticks it- self from the block and falls from rest to the ground. What is the resulting period T of the block's oscillation after the sep- aration occurs? For the limit check, investigate what happens to T if the block+clay only need to be lowered through an extremely short distance (d → 0) before they can be released motionlessly. = ✪ 4% =
This relates the initial speed of the pendulum box to the height that it goes: V =squr 2 g h . The numbers: g = 9.81 m/s2 h = 3.6 cm V = squr 2 × 9.81 × 3.6 = 8.4 Correct the calculation or the answer
A spring with spring constant 29 N/m is compressed a distance of 9.0 cm by a ball with a mass of 206.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 9.0 cm and is also released, leaving the spring at point A. Each object travels up the incline shown in the figure before coming to rest momentarily. Assume the ball rolls, but ignore other effects of friction. (Assume the ball rolls without slipping up the incline until it comes to rest.) (a) How high above the starting position is the ball when it comes to rest momentarily? m(b) How high above the starting position is the block when it comes to rest momentarily?
A 10-kilogram block is dropped from point A as shown. The rail is frictionless except for the 6 m long B and C parts. The block slides down the rail and hits a pedestrian with k = 2250 N / m and stops for a moment by compressing the spring by 30 cm according to the balance position. Find the kinetic friction coefficient between the B and C part of the rail and the block.
As shown in the figure below, a box of mass m = 9.80 kg is sliding across a horizontal frictionless surface with an initial speed vi = 2.70 m/s when it encounters a spring of constant k = 2700 N/m. The box comes momentarily to rest after compressing the spring some amount xc. Determine the final compression xc (in m) of the spring.
An 0.80-kg block is held in place against the spring by a 67-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v1=1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v2=1.9 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.39. The velocity of the block is v3=1.4 m/s at C. The block moves on to D, where it stops. The spring constant of the spring is closest to V2 V3 V4 A h smooth BErough C | ES >|
A spring with spring constant 23 N/m is compressed a distance of 8.0 cm by a ball with a mass of 219.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 8.0 cm and is also released, leaving the spring at point A. Assume the ball rolls, but ignore other effects of friction. (Assume that the ball is a solid ball.) (a) What is the speed of the ball at point B?(b) What is the speed of the block at point B?
If a 4-kg block is placed against the spring and the spring is released, what will be the speed of the block when it separates from the spring at x =0? Neglect any friction in the problem.
You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1300 kgkg car moving at 0.66 m/sm/s is to compress the spring no more than 7.6×10−2 mm before stopping. 1. What should be the force constant of the spring? Assume that the spring has negligible mass. Express your answer using two significant figures.
It takes a flea 1.25 × 10−3 s to reach a peak speed of 0.757 m/s. Mass of the flea is 0.462 × 10−6 kg and insect muscle has a maximum output of 56.4 W/kg. If 20.0% of the flea’s weight is muscle, what is the muscular power output of the flea?