# Solving Spring Tray Problem: Height Above Point A When Ball Leaves Tray

• Punkyc7
In summary, a 1.5 kg horizontal uniform tray is attached to a vertical ideal spring with a force constant of 185N/m. The tray also has a 275 g metal ball on it and can oscillate up and down. The tray is pushed down 15 cm below its equilibrium point, point A, and released from rest. The question is asking how high above point A the tray will be when the metal ball leaves it. The equations f=-kx and E=.5 mv^2+.5 k A^2 are used to find the answer, but setting mg=-kx did not lead to the correct solution. It is determined that the ball leaves the tray when the normal force on it is zero. Further
Punkyc7
A 1.5 kg horizontaal uniform tray is attached to a vertical ideal spring of force constant 185N/m and a 275 g metal ball is in the tray. The spring is below the tray, so it can oscillate up and down. The tray is then pushed down 15 cm below its equilibrium point called point A and released from rest.

How high above point A will the tray be when the metal ball leaves the tray.

Equations

f=-kx
E=.5 mv^2+.5 k A^2

Im thinking that this will occur when the normal force on the ball is zero.

so i set up the mg=-kx and solved for x but that didnt lead me too the right answer.

Any advice would be greatly appreciated.

Punkyc7 said:
Im thinking that this will occur when the normal force on the ball is zero.
And when is the normal force zero on the ball? What forces act on the ball? What is its acceleration till it moves together with the tray?

ehild

## 1. What is the purpose of solving the Spring Tray Problem?

The purpose of solving the Spring Tray Problem is to determine the height above Point A at which a ball will leave the tray when it is launched with a spring mechanism. This problem is often used in physics and engineering to model projectile motion and calculate the trajectory of an object.

## 2. How is the height above Point A calculated in the Spring Tray Problem?

The height above Point A is calculated using the principles of kinematics and projectile motion. This involves considering the initial velocity of the ball, the angle at which it is launched, and the effects of gravity on its motion. By solving equations of motion, the height above Point A can be determined.

## 3. What factors can affect the height above Point A in the Spring Tray Problem?

The height above Point A can be affected by various factors such as the initial velocity and angle of launch, the mass of the ball, the strength of the spring, and external factors like air resistance. These factors can impact the trajectory and distance traveled by the ball, thereby affecting the height above Point A.

## 4. How does the Spring Tray Problem relate to real-world applications?

The Spring Tray Problem has many real-world applications in fields such as sports, engineering, and physics. For example, it can be used to predict the trajectory of a thrown ball in sports like baseball or to determine the optimal angle for launching a projectile in engineering designs. It also has applications in understanding the motion of celestial bodies in astronomy.

## 5. Are there any limitations to solving the Spring Tray Problem?

Like any mathematical model, there are limitations to solving the Spring Tray Problem. It assumes a perfectly elastic collision between the ball and the tray, neglects air resistance, and assumes a constant gravitational force. In real-world scenarios, these factors may not hold true, and therefore, the calculated height above Point A may have some degree of error.

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