A 1.5 kg block initially at rest is launched by a horizontal spring with a spring constant of \( k = 175 \, \text{N/m} \). The spring is initially compressed a distance of 25 cm from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height \( h \) as shown below. Apply the Conservation of Energy Theorem to determine:a. The object's launch velocity at the spring's point of equilibrium in m/s.b. The maximum height reached by the block (\( h \)) in meters.c. Determine the impulse delivered by the spring in kg-m/s. (Hint: consider the initial and final locations as \( x_i = -25 \, \text{cm} \) and \( x_f = 0 \, \text{cm} \)).d. Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds.e. Determine the average power delivered by the spring in watts.**Diagram Explanation:**- The diagram features a spring attached to a block with a mass of 1.5 kg. The block is launched from a horizontal surface by the compressed spring.- The spring's equilibrium position is marked, and the compression distance is noted as \( x_i = -25 \, \text{cm} \).- The block moves up a frictionless incline and reaches the maximum height \( h \).**List of Numerical Options:**1. 12.232. 0.25473. 2.7004. 24.595. 7.5836. 36.437. 21.898. 29.589. 0.187010. 0.37211. 4.05012. 10.4313. 1.58014. 5.40015. 32.58 **Physics Problem: Spring Launch**A 1.5 kg block initially at rest is launched by a horizontal spring with a spring constant of \( k = 175 \, \text{N/m} \). The spring is initially compressed a distance of 25 cm from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height \( h \) as shown. Apply the Conservation of Energy Theorem to determine:a. The object's launch velocity at the spring's point of equilibrium in m/s.b. The maximum height reached by the block (\( h \)) in meters.c. Determine the impulse delivered by the spring in kg-m/s. (Hint: consider the initial and final locations as \( x = -25 \, \text{cm} \) and \( x = 0 \, \text{cm} \) ).d. Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds.e. Determine the average power delivered by the spring in watts.**Diagram Explanation:**- The diagram shows a spring with a mass of 1.5 kg attached at the end. The spring is initially compressed by 25 cm. - There is a frictionless incline, and the block ascends this incline to reach a maximum height \( h \).**Multiple Choice Answers:**1. 12.232. 0.25473. 2.7004. 24.595. 7.5886. 36.437. 21.808. 26.589. 0.187010. 0.37211. 4.05012. 10.4313. 1.58014. 5.49015. 32.58

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A 1.5 kg block initially at rest, is launched by a horizontal spring with a spring constant of k-175 N/m. The spring is initially compressed a distance of 25 em from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height of has shown below. Apply the Conservation of Energy Theorem to determine, a. The object's launch velocity at the spring's point of equilibrium in m/s. b. The maximum height reached by the block (h) in meters. e. Determine the impulse delivered by the spring in kg-m/s. d. (Hint: consider the initial and final locations as x=-25 cm and x=0 cm). Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds. c. Determine the average power delivered by the spring in watts. hud 1.5-kg x= - 25 cm 0 1. 2 3.

A 1.5 kg block initially at rest, is launched by a horizontal spring with a spring constant of k-175 N/m. The spring is initially compressed a distance of 25 em from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height of has shown below. Apply the Conservation of Energy Theorem to determine, a. The object's launch velocity at the spring's point of equilibrium in m/s. b. The maximum height reached by the block (h) in meters. e. Determine the impulse delivered by the spring in kg-m/s. d. (Hint: consider the initial and final locations as x=-25 cm and x=0 cm). Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds. c. Determine the average power delivered by the spring in watts. hud 1.5-kg x= - 25 cm 0 1. 2 3.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 50PQ: A jack-in-the-box is actually a system that consists of an object attached to the top of a vertical...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

A 1.5 kg block initially at rest is launched by a horizontal spring with a spring constant of \( k = 175 \, \text{N/m} \). The spring is initially compressed a distance of 25 cm from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height \( h \) as shown below. Apply the Conservation of Energy Theorem to determine:

a. The object's launch velocity at the spring's point of equilibrium in m/s.

b. The maximum height reached by the block (\( h \)) in meters.

c. Determine the impulse delivered by the spring in kg-m/s.
(Hint: consider the initial and final locations as \( x_i = -25 \, \text{cm} \) and \( x_f = 0 \, \text{cm} \)).

d. Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds.

e. Determine the average power delivered by the spring in watts.

**Diagram Explanation:**
- The diagram features a spring attached to a block with a mass of 1.5 kg. The block is launched from a horizontal surface by the compressed spring.
- The spring's equilibrium position is marked, and the compression distance is noted as \( x_i = -25 \, \text{cm} \).
- The block moves up a frictionless incline and reaches the maximum height \( h \).

**List of Numerical Options:**
1. 12.23
2. 0.2547
3. 2.700
4. 24.59
5. 7.583
6. 36.43
7. 21.89
8. 29.58
9. 0.1870
10. 0.372
11. 4.050
12. 10.43
13. 1.580
14. 5.400
15. 32.58

**Physics Problem: Spring Launch**

A 1.5 kg block initially at rest is launched by a horizontal spring with a spring constant of \( k = 175 \, \text{N/m} \). The spring is initially compressed a distance of 25 cm from equilibrium. After being launched, the block travels toward the top of a frictionless incline and comes to rest after reaching a maximum height \( h \) as shown. Apply the Conservation of Energy Theorem to determine:

a. The object's launch velocity at the spring's point of equilibrium in m/s.

b. The maximum height reached by the block (\( h \)) in meters.

c. Determine the impulse delivered by the spring in kg-m/s.
(Hint: consider the initial and final locations as \( x = -25 \, \text{cm} \) and \( x = 0 \, \text{cm} \) ).

d. Determine the average force exerted by the spring on the block (in Newtons) if the time of contact equals 0.185 seconds.

e. Determine the average power delivered by the spring in watts.

**Diagram Explanation:**
- The diagram shows a spring with a mass of 1.5 kg attached at the end. The spring is initially compressed by 25 cm.
- There is a frictionless incline, and the block ascends this incline to reach a maximum height \( h \).

**Multiple Choice Answers:**
1. 12.23
2. 0.2547
3. 2.700
4. 24.59
5. 7.588
6. 36.43
7. 21.80
8. 26.58
9. 0.1870
10. 0.372
11. 4.050
12. 10.43
13. 1.580
14. 5.490
15. 32.58

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