# Problem: A child's toy 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 spring constant K, the ball has a mass M, and the ramp rises a height Y above the table, the surface of which is a height H above the floor.Initially, the spring rests at its equilibrium length. The spring then is compressed a distance S, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle THETA with respect to the horizontal.Throughout this problem, ignore friction and air resistance.1) Calculate Vr, the speed of the ball when it leaves the launching ramp.Express the speed of the ball in terms of K, S, M, Y, G, and/or .H2) With what speed will the ball hit the floor, Vf?Express the speed in terms of K, S, M, Y, G, and/or .H

###### FREE Expert Solution

Conservation of energy:

$\overline{){\mathbf{P}}{{\mathbf{E}}}_{{\mathbf{i}}}{\mathbf{+}}{\mathbf{K}}{{\mathbf{E}}}_{{\mathbf{i}}}{\mathbf{=}}{\mathbf{P}}{{\mathbf{E}}}_{{\mathbf{f}}}{\mathbf{+}}{\mathbf{K}}{{\mathbf{E}}}_{{\mathbf{f}}}}$

1)

PE = mgH and KE = 1/2mv2

89% (382 ratings) ###### Problem Details

A child's toy 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 spring constant K, the ball has a mass M, and the ramp rises a height Y above the table, the surface of which is a height H above the floor.

Initially, the spring rests at its equilibrium length. The spring then is compressed a distance S, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle THETA with respect to the horizontal.

Throughout this problem, ignore friction and air resistance.

1) Calculate Vr, the speed of the ball when it leaves the launching ramp.

Express the speed of the ball in terms of K, S, M, Y, G, and/or .H

2) With what speed will the ball hit the floor, Vf?

Express the speed in terms of K, S, M, Y, G, and/or .H

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Conservative Forces & Inclined Planes concept. You can view video lessons to learn Conservative Forces & Inclined Planes. Or if you need more Conservative Forces & Inclined Planes practice, you can also practice Conservative Forces & Inclined Planes practice problems.

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Based on our data, we think this problem is relevant for Professor Reyes' class at UCF.