Calculating horizontal difference in spring-ball situation

In summary, the conversation is about calculating the horizontal distance a ball will travel when a compressed spring is aimed 25° from the horizontal. The first part involved finding the speed at which the ball leaves the spring when aimed vertically, which was calculated to be 5.11 m/s. The second part involves using relevant equations, such as v2=v02+2ax and Vx=Vcosθ, to find the displacement. The attempt at a solution involved setting the final velocity to zero and using the initial velocity from part one, but resulted in an incorrect answer of 1.15 m. The correct answer is 2.04 m, which can be found by breaking the motion into horizontal and vertical components and using the SUV
  • #1
foreverconfused
1
0
1.Problem The problem is: calculate the horizontal distance the ball will travel if the same spring is aimed 25° from the horizontal. This is the second part.

The first part was: a small steel ball bearing with a mass of 21 g is on a short compressed spring. When aimed vertically and suddenly released, the spring sends the bearing to a height of 1.33 m. Calculate the speed at which the ball leaves the spring (my correct answer was 5.11 m/s)
2.Relevant equations: Just like the first part I tried using v2=v02+2ax since that still seems relevant. I know I should be incorporating Vx=Vcosθ but I'm not sure how. 3.The attempt at a solution: I set the final velocity to zero and the initial velocity as the answer I had gotten from part one. I set the gravity as acceleration as I had in part one and solved for x (displacement).

0=5.112+2*9.81*x
then x=1.15 m which I know isn't right.

The answer is 2.04 m, I just don't know how to get that.

Also this is my first post so please let me know if I'm missing any information.
 
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  • #2
You need to break the motion into horizontal and vertical components.
Are you familiar with the SUVAT equations?
What facts do you know about the two components of movement in this problem?
 

1. How is the horizontal distance calculated in a spring-ball situation?

The horizontal distance in a spring-ball situation is calculated by using the formula x = v₀t + (1/2)at², where x is the distance, v₀ is the initial velocity, t is the time, and a is the acceleration. This formula is derived from the kinematic equations of motion.

2. What is the significance of calculating the horizontal difference in a spring-ball situation?

Calculating the horizontal difference helps determine the displacement of the ball from its initial position. This information is important in understanding the trajectory of the ball and predicting where it will land. It also allows for the calculation of other variables such as the velocity and acceleration of the ball.

3. Can the horizontal distance in a spring-ball situation be negative?

Yes, the horizontal distance can be negative. This indicates that the ball has moved in the opposite direction of the initial velocity. For example, if the ball is thrown in the negative x-direction, the horizontal distance will be negative.

4. Is air resistance taken into account when calculating the horizontal distance in a spring-ball situation?

In most cases, air resistance is negligible and can be ignored when calculating the horizontal distance in a spring-ball situation. However, if the ball is moving at high speeds or over long distances, then air resistance may need to be considered in the calculation.

5. How does the mass of the ball affect the horizontal distance in a spring-ball situation?

The mass of the ball does not directly affect the horizontal distance in a spring-ball situation. The distance is primarily dependent on the initial velocity and time. However, the mass of the ball may indirectly affect the horizontal distance if it affects the acceleration of the ball due to factors such as air resistance or friction.

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