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27 problems tagged with Spring
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?
P0464
Beginner Mechanics › Work and EnergySpring Gun Horizontal Launch
A spring in a spring gun has a spring constant $k = 80$ N/m. The trigger holds the spring compressed by 5 cm. A 10 g bullet is placed in the barrel against the spring. The barrel is horizontal.
P0465
Beginner Mechanics › Work and EnergyBlock Dropped onto a Vertical Spring
A 2.0 kg block is dropped from a height of 0.40 m onto a vertical spring standing on the ground. The spring has a spring constant $k = 2000$ N/m.
P0775
Advanced Mechanics › Waves and SoundDamped Oscillation with Friction and a Wall
An object of mass $m$ on a horizontal surface with friction coefficient $\mu$ is subject to a restoring force $F=-kx$. There is a perfectly elastic wall at the origin $x=0$. The object is released from rest at $x=x_1 > 0$. Let $x_s = \mu mg/k$ be the magnitude of the displacement where the spring force equals the friction force.
- Find the total time until the object stops permanently.
- Find the final resting position of the object.
- Find the total work done by the object against friction.
P0776
Advanced Mechanics › Waves and SoundMass on Spring Dropping with Acceleration
An object of mass $m$ is attached to a light spring with spring constant $k$, which is fixed to the ceiling. Initially, the object rests on a plate P, the spring is unstretched, and its axis is vertical.
- Find the maximum extension $L$ of the spring when the plate starts to move downwards with a constant acceleration $a$.
- Plot the function $L$ versus $a$.
P0467
Beginner Mechanics › Work and EnergySpring Extension from Dropped Mass
An object is attached to a vertical spring. When lowered slowly, it reaches an equilibrium position where the spring is extended by a length $d$.
P0555
Beginner Mechanics › Work and EnergyBlock Compressing a Spring with Friction
A block of mass $m$ slides on a horizontal floor with a coefficient of kinetic friction $\mu_k$. It collides head-on with a horizontal spring of spring constant $k$. The block comes to rest after compressing the spring by a distance $x$.
- What is the work done by the spring force on the block?
- What is the increase in thermal energy of the block-floor system?
- What was the block's speed, $v$, just as it reached the spring?
P0468
Beginner Mechanics › Work and EnergyVertical Spring Gun Spring Constant
A 5.0 g bullet is fired vertically upward by a spring gun. The spring must be compressed by at least 10 cm for the bullet to reach a target 20 m high (measured from the muzzle).
P0563
Beginner Mechanics › Work and EnergyBlocks and Spring System Energy Conservation
A block of mass $M$ rests on a frictionless horizontal surface. It is connected to a fixed spring of constant $k$. A string attached to this block passes over a frictionless, massless pulley and is connected to a hanging block of mass $2M$. The system is released from rest with the spring in its relaxed (equilibrium) position.
- Find the combined kinetic energy of the two blocks when the hanging block has fallen a distance $d$.
- Find the kinetic energy of the hanging block at that same distance $d$.
- Find the maximum distance $d_{max}$ the hanging block falls before momentarily stopping.
P0486
Beginner Mechanics › Work and EnergyBlock Pushed by Spring on Rough Surface
As shown, a block of mass $m$ is on a horizontal surface with a coefficient of kinetic friction $\mu_k$. It is pushed by a compressed spring with spring constant $k$. After leaving the spring (at the spring's equilibrium position), the block slides a distance $d$ before stopping.
- What is the object's maximum kinetic energy?
- What was the initial compression length of the spring?
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