Maximum height of a spring toy

In summary, by calculating the vertical component of the initial velocity and using it in the equation for vertical motion, the maximum height reached by the spring toy is 0.26 m [up]. This is an improvement from the previous calculation that did not include the angle provided in the problem.
  • #1
Evangeline101
112
5

Homework Statement


A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy?

Homework Equations



Δ[/B]dv = v1Δt + 1/2aΔt2

The Attempt at a Solution


[/B]
Calculate time:

Δt = 2.3 m/s / 9.8m/s2

= 0.23 s

Now calculate vertical motion:
Δdv = v1Δt + 1/2aΔt2 *for vertical motion, let (up) be positive

Δdv = (2.3 m/s) x (0.23s) + 1/2 (-9.8 m/s2) x (0.23s)2

Δdv = 0.27 m [up]

The maximum height reached by the spring toy is 0.27 m [up].

Is this correct? I have a feeling I did it wrong because I did not use the angle they provided and only used the velocity.
 
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  • #2
Evangeline101 said:

Homework Statement


A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy?

Homework Equations



Δ[/B]dv = v1Δt + 1/2aΔt2

The Attempt at a Solution


[/B]
Calculate time:

Δt = 2.3 m/s / 9.8m/s2

= 0.23 s

Now calculate vertical motion:
Δdv = v1Δt + 1/2aΔt2 *for vertical motion, let (up) be positive

Δdv = (2.3 m/s) x (0.23s) + 1/2 (-9.8 m/s2) x (0.23s)2

Δdv = 0.27 m [up]

The maximum height reached by the spring toy is 0.27 m [up].

Is this correct? I have a feeling I did it wrong because I did not use the angle they provided and only used the velocity.

No, it's not correct. Why didn't you calculate the vertical component of the initial velocity?
 
  • #3
SteamKing said:
No, it's not correct. Why didn't you calculate the vertical component of the initial velocity?

Okay, so I did it again with the vertical component of initial velocity.

Calculate vertical component of initial velocity:

V1v = v1sinθ

V1v = (2.3 m/s) sin 78°

V1v = 2.25 m/s [up]

Calculate time:

Δt = 2.3 m/s / 9.8m/s2

= 0.23 s

Calculate vertical motion:
Δdv = v1Δt + 1/2aΔt2 *for vertical motion, let (up) be positive

Δdv = (2.25 m/s) x (0.23s) + 1/2 (-9.8 m/s2) x (0.23s)2

Δdv = 0.26 m [up]

The maximum height reached by the spring toy is 0.26 m [up].

Is this better?
 
  • #4
Evangeline101 said:
Okay, so I did it again with the vertical component of initial velocity.

Calculate vertical component of initial velocity:

V1v = v1sinθ

V1v = (2.3 m/s) sin 78°

V1v = 2.25 m/s [up]

Calculate time:

Δt = 2.3 m/s / 9.8m/s2

= 0.23 s

Calculate vertical motion:
Δdv = v1Δt + 1/2aΔt2 *for vertical motion, let (up) be positive

Δdv = (2.25 m/s) x (0.23s) + 1/2 (-9.8 m/s2) x (0.23s)2

Δdv = 0.26 m [up]

The maximum height reached by the spring toy is 0.26 m [up].

Is this better?
Much better.
 
  • #5
SteamKing said:
Much better.

Thanks for the help :)
 

1. What is the maximum height a spring toy can reach?

The maximum height a spring toy can reach depends on a few factors such as the strength and elasticity of the spring, the weight and shape of the toy, and the initial force used to compress the spring. Generally, most spring toys can reach heights of 1-2 feet.

2. How is the maximum height of a spring toy calculated?

The maximum height of a spring toy is calculated by using the mathematical formula for potential energy: PE = 1/2 kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement of the spring. This formula takes into account the strength and elasticity of the spring as well as the initial force applied to it.

3. Can the maximum height of a spring toy be increased?

Yes, the maximum height of a spring toy can be increased by using a stronger and more elastic spring, reducing the weight of the toy, and applying a greater initial force to compress the spring. However, there is a limit to how high a spring toy can reach, as it is limited by the strength and elasticity of the spring.

4. What happens if the maximum height of a spring toy is exceeded?

If the maximum height of a spring toy is exceeded, the spring will not be able to support the weight of the toy and it will either stop bouncing or collapse. The spring may also become permanently deformed or break if the force applied to it is too great.

5. Are there any safety precautions to consider when using a spring toy?

Yes, it is important to use caution when using a spring toy, especially if trying to reach maximum height. Make sure to use a toy that is appropriate for your age and size, and always follow the manufacturer's instructions. Also, be aware of your surroundings and avoid using the toy near objects or people that could be injured if the toy were to accidentally hit them.

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