A spring-loaded toy gun is used to shoot a ball of mass m = 1.50 kg straight up in the air, as shown in (Figure 1). The spring has spring constant k = 667 N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y = 0 and then released, the ball reaches a maximum height hmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis. Figure Imax O y=0 1 of 1 Part B Find vm the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y = 0). ▸ View Available Hint(s) Um= Submit Part C Templates Symbols undo redo reset keyboard shortcuts help, Find the maximum height hmaxof the ball. Express your answer numerically, in meters. ▸ View Available Hint(s) hmax Submit Part D Templates Symbols undo redo reset keyboard shortcuts help, m/s m Which of the following actions, if done independently, would increase the maximum height reached by the ball? Check all that apply. Submit Request Answer reducing the spring constant k increasing the spring constant k decreasing the distance the spring is compressed increasing the distance the spring is compressed decreasing the mass of the ball increasing the mass of the ball tilting the spring gun so that it is at an angle 0 < 90 degrees from the horizontal
A spring-loaded toy gun is used to shoot a ball of mass m = 1.50 kg straight up in the air, as shown in (Figure 1). The spring has spring constant k = 667 N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y = 0 and then released, the ball reaches a maximum height hmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis. Figure Imax O y=0 1 of 1 Part B Find vm the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y = 0). ▸ View Available Hint(s) Um= Submit Part C Templates Symbols undo redo reset keyboard shortcuts help, Find the maximum height hmaxof the ball. Express your answer numerically, in meters. ▸ View Available Hint(s) hmax Submit Part D Templates Symbols undo redo reset keyboard shortcuts help, m/s m Which of the following actions, if done independently, would increase the maximum height reached by the ball? Check all that apply. Submit Request Answer reducing the spring constant k increasing the spring constant k decreasing the distance the spring is compressed increasing the distance the spring is compressed decreasing the mass of the ball increasing the mass of the ball tilting the spring gun so that it is at an angle 0 < 90 degrees from the horizontal
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)...
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![### Spring-Loaded Toy Gun Physics Problem
A spring-loaded toy gun is used to shoot a ball of mass \( m = 1.50 \, \text{kg} \) straight up into the air, as shown in Figure 1. The spring has a spring constant \( k = 667 \, \text{N/m} \). If the spring is compressed a distance of 25.0 centimeters from its equilibrium position \( y = 0 \) and then released, the ball reaches a maximum height \( h_{\text{max}} \) (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y-axis.
#### Figure Explanation
The figure illustrates a vertical spring with a ball placed on top. The spring is compressed, illustrated by a downward arrow, and upon release, it propels the ball upwards to a maximum height \( h_{\text{max}} \), marked by an upward arrow. The spring's equilibrium position is labeled as \( y = 0 \).
### Part B
**Objective:** Find \( v_m \), the muzzle velocity of the ball (i.e., the velocity of the ball at the spring’s equilibrium position \( y = 0 \)).
**Input Field:**
- \( v_m = \) [Input box for answer] m/s
### Part C
**Objective:** Find the maximum height \( h_{\text{max}} \) of the ball.
**Input Field:**
- \( h_{\text{max}} = \) [Input box for answer] m
### Part D
**Objective:** Determine which actions, if done independently, would increase the maximum height reached by the ball.
**Options:**
- [ ] Reducing the spring constant \( k \)
- [ ] Increasing the spring constant \( k \)
- [ ] Decreasing the distance the spring is compressed
- [ ] Increasing the distance the spring is compressed
- [ ] Decreasing the mass of the ball
- [ ] Increasing the mass of the ball
- [ ] Tilting the spring gun so that it is at an angle \( \theta < 90 \) degrees from the horizontal
**Buttons:**
- Submit
- Request Answer
This exercise helps illustrate the principles of energy conversion and projectile motion in a controlled, frictionless environment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf6a08b4-8e75-478e-afb6-07a17515e38d%2Fde733366-4c59-4a9d-a858-51fa33a00b85%2Fxa9bd3o_processed.png&w=3840&q=75)
Transcribed Image Text:### Spring-Loaded Toy Gun Physics Problem
A spring-loaded toy gun is used to shoot a ball of mass \( m = 1.50 \, \text{kg} \) straight up into the air, as shown in Figure 1. The spring has a spring constant \( k = 667 \, \text{N/m} \). If the spring is compressed a distance of 25.0 centimeters from its equilibrium position \( y = 0 \) and then released, the ball reaches a maximum height \( h_{\text{max}} \) (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y-axis.
#### Figure Explanation
The figure illustrates a vertical spring with a ball placed on top. The spring is compressed, illustrated by a downward arrow, and upon release, it propels the ball upwards to a maximum height \( h_{\text{max}} \), marked by an upward arrow. The spring's equilibrium position is labeled as \( y = 0 \).
### Part B
**Objective:** Find \( v_m \), the muzzle velocity of the ball (i.e., the velocity of the ball at the spring’s equilibrium position \( y = 0 \)).
**Input Field:**
- \( v_m = \) [Input box for answer] m/s
### Part C
**Objective:** Find the maximum height \( h_{\text{max}} \) of the ball.
**Input Field:**
- \( h_{\text{max}} = \) [Input box for answer] m
### Part D
**Objective:** Determine which actions, if done independently, would increase the maximum height reached by the ball.
**Options:**
- [ ] Reducing the spring constant \( k \)
- [ ] Increasing the spring constant \( k \)
- [ ] Decreasing the distance the spring is compressed
- [ ] Increasing the distance the spring is compressed
- [ ] Decreasing the mass of the ball
- [ ] Increasing the mass of the ball
- [ ] Tilting the spring gun so that it is at an angle \( \theta < 90 \) degrees from the horizontal
**Buttons:**
- Submit
- Request Answer
This exercise helps illustrate the principles of energy conversion and projectile motion in a controlled, frictionless environment.
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