2. A block of mass 0.25 kg is pushed against a spring of spring constant 80 N/m. It can slide without friction along a board tilted at an angle 30º above horizontal. Initially the block is released from rest when the spring is compressed by a distance 0.3 m. a. What is the speed of the block when the block loses contact with the spring? This occurs when the spring is back to its relaxed length. 0 1.
2. A block of mass 0.25 kg is pushed against a spring of spring constant 80 N/m. It can slide without friction along a board tilted at an angle 30º above horizontal. Initially the block is released from rest when the spring is compressed by a distance 0.3 m. a. What is the speed of the block when the block loses contact with the spring? This occurs when the spring is back to its relaxed length. 0 1.
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![**Physics Problem Explanation**
**Problem Statement:**
*What is the distance the block will slide along the ramp before it starts coming back down? Give the distance from the initial position of the block when the spring was compressed.*
To solve this problem, let's break down the steps necessary to find the distance the block will slide along the ramp before it starts coming back down. Here is a detailed explanation suitable for educational purposes:
1. **Understanding the System:**
- A block is initially at rest, compressing a spring at the bottom of a ramp.
- When the spring is released, the block is propelled up the ramp due to the potential energy stored in the compressed spring.
2. **Energy Conservation:**
- The total mechanical energy in this system is conserved if we ignore friction and air resistance.
- Initially, the block has maximum elastic potential energy and no kinetic energy (assuming it starts from rest).
3. **Calculating Potential Energy:**
- The elastic potential energy \( U_{spring} \) in the spring is given by:
\[
U_{spring} = \frac{1}{2} k x^2
\]
where \( k \) is the spring constant, and \( x \) is the compression distance of the spring.
4. **Transferring Energy to Kinetic and Gravitational Potential Energy:**
- As the block moves up the ramp, the elastic potential energy is converted into kinetic energy and gravitational potential energy.
- At the highest point on the ramp, all the spring's elastic potential energy will be converted into gravitational potential energy:
\[
U_{gravity} = m g h
\]
where \( m \) is the mass of the block, \( g \) is the gravitational acceleration, and \( h \) is the vertical height the block reaches.
5. **Using Trigonometry to Find the Distance Along the Ramp:**
- The relationship between the vertical height \( h \) and the distance along the ramp \( d \) is:
\[
h = d \sin(\theta)
\]
where \( \theta \) is the angle of the incline.
- Rearranging to find \( d \):
\[
d = \frac{h}{\sin(\theta)}
\]
6. **Final Calculation:**
- Energy conservation gives us:
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Transcribed Image Text:**Physics Problem Explanation**
**Problem Statement:**
*What is the distance the block will slide along the ramp before it starts coming back down? Give the distance from the initial position of the block when the spring was compressed.*
To solve this problem, let's break down the steps necessary to find the distance the block will slide along the ramp before it starts coming back down. Here is a detailed explanation suitable for educational purposes:
1. **Understanding the System:**
- A block is initially at rest, compressing a spring at the bottom of a ramp.
- When the spring is released, the block is propelled up the ramp due to the potential energy stored in the compressed spring.
2. **Energy Conservation:**
- The total mechanical energy in this system is conserved if we ignore friction and air resistance.
- Initially, the block has maximum elastic potential energy and no kinetic energy (assuming it starts from rest).
3. **Calculating Potential Energy:**
- The elastic potential energy \( U_{spring} \) in the spring is given by:
\[
U_{spring} = \frac{1}{2} k x^2
\]
where \( k \) is the spring constant, and \( x \) is the compression distance of the spring.
4. **Transferring Energy to Kinetic and Gravitational Potential Energy:**
- As the block moves up the ramp, the elastic potential energy is converted into kinetic energy and gravitational potential energy.
- At the highest point on the ramp, all the spring's elastic potential energy will be converted into gravitational potential energy:
\[
U_{gravity} = m g h
\]
where \( m \) is the mass of the block, \( g \) is the gravitational acceleration, and \( h \) is the vertical height the block reaches.
5. **Using Trigonometry to Find the Distance Along the Ramp:**
- The relationship between the vertical height \( h \) and the distance along the ramp \( d \) is:
\[
h = d \sin(\theta)
\]
where \( \theta \) is the angle of the incline.
- Rearranging to find \( d \):
\[
d = \frac{h}{\sin(\theta)}
\]
6. **Final Calculation:**
- Energy conservation gives us:
\
Transcribed Image Text:### Problem Statement
A block of mass 0.25 kg is pushed against a spring of spring constant 80 N/m. It can slide without friction along a board tilted at an angle of 30° above horizontal. Initially, the block is released from rest when the spring is compressed by a distance of 0.3 m.
**a. What is the speed of the block when the block loses contact with the spring?**
*This occurs when the spring is back to its relaxed length.*
### Diagram Description
The accompanying diagram shows a block on an inclined plane equipped with a spring. The inclined plane is at an angle \( \theta \) of 30° from the horizontal. The block presses against the spring, which is initially compressed. A gravitational force \( g \) acts downward, and an arrow indicates the direction in which the block will move when released.
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