How to Calculate the Velocity and Impact Speed of a Ball Launched by a Spring?

In summary, the problem involves a child's game with a block attached to a table with a suction cup, a spring with a constant k, a ball with mass m, and a launching ramp. The spring is compressed a distance S to launch the ball, which then has a velocity and angle with respect to the horizontal. The goal is to calculate the velocity of the ball when it leaves the ramp and when it hits the floor. To solve this, conservation of energy can be used, with the equation 1/2 mvf^2 + mgh = 1/2 mvi^2 + mgh. With the given values, the masses cancel out and the final velocity can be solved for using the
  • #1
bmandrade
63
0

Homework Statement



A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a constant k. the ball has a mass m, and the ramp raises a height h. The spring is compressed a distance S in order to launch the ball. when the ball leaves the launching ramp its velocity makes and angle with respect to the horizontal.

1 Calculate the velocity of the ball when its leaves the launching ramp (both the magnitude and the direction. Be sure to specify your coordinate system)

2. The spring constant = 1000.0 N/m the spring compression is 4. cm the ball's mass is 55 g, the height of the ramp is 15 cm and the top of the table is 1.2 m above the floor. With what speed will the ball hit the floor?



Homework Equations


Delta y = Vft+1/2gt2
speed=distance/time

The Attempt at a Solution



I really do not have a clue where to start I have been thinking on how to solve it but all i have done is write down some equations that may be helpful but i really don't know if they are helpful in this problem. Can someone please help me? thanks
 
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  • #2
bmandrade said:

Homework Statement



1 Calculate the velocity of the ball when its leaves the launching ramp (both the magnitude and the direction. Be sure to specify your coordinate system)

2. The spring constant = 1000.0 N/m the spring compression is 4. cm the ball's mass is 55 g, the height of the ramp is 15 cm and the top of the table is 1.2 m above the floor. With what speed will the ball hit the floor?

Have you considered conservation of energy?
 
  • #3
yes i had that equation KEf+PEf=KEi+PEi

so 1/2 mvf2 + mgh = 1/2 mvi2 + mgh

so in this case masses cancel and i would have to solve for vf
 
  • #4
bmandrade said:
yes i had that equation KEf+PEf=KEi+PEi

so 1/2 mvf2 + mgh = 1/2 mvi2 + mgh

so in this case masses cancel and i would have to solve for vf

Sounds fine by me.
 
  • #5
ok well i know that 1/2mvi^2 = 0 and the mgh final should be 0 too

in that case vf= square root of 2gh

however i got stuck because i there is no value given for h is there a way i can find h or am i suppose to have another equation
 

FAQ: How to Calculate the Velocity and Impact Speed of a Ball Launched by a Spring?

1. What is the "spring and ball problem"?

The "spring and ball problem" is a physics problem that involves a spring attached to a ball and a fixed point. The ball is pulled down and released, causing the spring to stretch and the ball to bounce up and down.

2. What are the factors that affect the motion of the ball in the "spring and ball problem"?

The motion of the ball in the "spring and ball problem" is affected by the mass of the ball, the stiffness of the spring, and the gravitational force acting on the ball.

3. How does the spring constant affect the motion of the ball in the "spring and ball problem"?

The spring constant, also known as the stiffness of the spring, directly affects the frequency of the ball's oscillations. A higher spring constant will result in a higher frequency and a shorter period of oscillation.

4. What is the relationship between the amplitude and energy in the "spring and ball problem"?

The amplitude, or maximum displacement, of the ball is directly proportional to the energy stored in the spring. As the amplitude increases, so does the energy of the system.

5. How can the "spring and ball problem" be applied in real-life situations?

The principles of the "spring and ball problem" can be applied in many real-life situations, such as in the design of suspension systems for vehicles or in the study of earthquakes and other natural oscillations. It is also commonly used in physics demonstrations and experiments to illustrate concepts such as energy conservation and simple harmonic motion.

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