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Browse Problems
20 problems tagged with Spring in Work and Energy
P0538
Intermediate Mechanics › Work and EnergyCanister Launched by Spring on Incline
A spring with constant $k$ is at the top of a frictionless incline of angle $\theta$. The lower end of the incline is a distance $D$ from the spring's relaxed position. A canister of mass $m$ is pushed against the spring until it is compressed by a distance $x$ and released from rest.
- What is the speed of the canister, $v_1$, at the instant the spring returns to its relaxed length?
- What is the speed of the canister, $v_2$, when it reaches the lower end of the incline?
P0540
Intermediate Mechanics › Work and EnergyBlock Sliding on Incline into Spring
A block of mass $m$ slides from rest a distance $d$ down a frictionless incline at an angle $\theta$ to the horizontal. It then runs into a spring of spring constant $k$. When the block momentarily stops, it has compressed the spring by a distance $x$.
- What is the distance $d$?
- What is the distance the spring is compressed from its equilibrium position when the block's speed is greatest?
P0541
Intermediate Mechanics › Work and EnergySpring-Gun Projectile Target Practice
A spring-loaded gun is mounted horizontally on a table. A child tries to hit a small target box on the floor, located a horizontal distance $D$ from the edge of the table. In the first attempt, the spring is compressed by a distance $x_1$, and the marble falls short of the center of the box by a distance $S_1$. Assume no friction.
P0454
Beginner Mechanics › Work and EnergyElastic Potential Energy of a Compressed Spring
A force of $F = 120$ N is required to compress a spring by $x_1 = 4$ cm.
P0455
Beginner Mechanics › Work and EnergyChange in Elastic Potential Energy
A spring with a natural length of $20$ cm and a spring constant of $k = 1000$ N/m is stretched.
- What is the increase in elastic potential energy when the spring is stretched from its natural length to $25$ cm?
- What is the increase in elastic potential energy when it is further stretched from $25$ cm to $30$ cm?
- Are these two increases in energy equal?
P0457
Beginner Mechanics › Work and EnergyVelocity of an Oscillating Mass on a Spring
A light spring with a spring constant $k = 360$ N/m has one end fixed. The other end is attached to a small ball of mass $m = 100$ g, which is placed on a smooth horizontal surface. The ball is pulled from its equilibrium position to a displacement of $x_1 = 10$ cm and then released from rest.
P0461
Beginner Mechanics › Work and EnergyBlock, Spring, and Friction on a Surface
A 2.0 kg block on a horizontal surface is pushed against a light horizontal spring (spring constant 200 N/m), compressing it by 15 cm. The block is then released from rest. After leaving the spring (at its equilibrium position), the block slides 60 cm before coming to a stop.
P0549
Beginner Mechanics › Work and EnergyBlock Dropped onto a Vertical Spring
A block of mass $m$ is dropped onto a relaxed vertical spring with a spring constant $k$. The block attaches to the spring and compresses it by a maximum distance $x_m$ before momentarily stopping. Let $v_i$ be the speed of the block just before it hits the spring. Friction is negligible.
- What is the work $W_g$ done on the block by the gravitational force during the compression phase (from initial contact to maximum compression)?
- What is the work $W_s$ done on the block by the spring force during the compression phase?
- What is the speed $v_i$ of the block just before it hits the spring, in terms of $m, k, g,$ and $x_m$?
- If the speed at impact is doubled to $v'_i = 2v_i$, what is the new maximum compression $x'_m$ of the spring?
P0550
Beginner Mechanics › Work and EnergyBlock Launched by a Spring on an Incline
A block of mass $m$ is placed against a spring with spring constant $k$ on a frictionless incline with an angle of inclination $\theta$. The block is not attached to the spring. The spring is initially compressed by a distance $x$ from its equilibrium position. The block is then released from rest.
- What is the initial elastic potential energy $U_e$ stored in the compressed spring?
- What is the change in the gravitational potential energy $\Delta U_g$ of the block-Earth system as the block moves from the release point to its highest point on the incline?
- How far $d$ along the incline does the block travel from its release point to its highest point?
P0551
Beginner Mechanics › Work and EnergyBlock on an Incline with a Spring
A block of mass $m$ on a frictionless incline of angle $\theta$ is connected by a cord that runs over a massless, frictionless pulley to a light spring of spring constant $k$. The block is released from rest when the spring is unstretched.
- What is the speed $v$ of the block after it has moved a distance $d_1$ down the incline?
- How far $d_{max}$ down the incline does the block slide before momentarily stopping?
- What are the magnitude and direction of the block's acceleration at the instant it momentarily stops?
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