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One day when you come into lab, you see a spring-loaded
Chapter 4, Problem 4.29(choose chapter or problem)
One day when you enter the lab, you see a spring-loaded wheel that can launch a ball straight up. To do so, you place the ball in a cup on the wheel's rim, turn the wheel to stretch the spring, then release. The wheel rotates through an angle \(\Delta\theta\), then hits a stop when the cup is level with the axle and pointing straight up. The cup stops, but the ball flies out and keeps going. You're told that the wheel has been designed to have constant angular acceleration as it rotates through \(\Delta\theta\). The lab assignment is first to measure the wheel's angular acceleration. Then the lab instructor is going to place a target at height \(h\) above the point where the ball is launched. Your task will be to launch the ball so that it just barely hits the target.
a. Find an expression in terms of quantities that you can measure for the angle \(\Delta \theta\) that launches the ball at the correct speed.
b. Evaluate \(\Delta \theta\) if the wheel's diameter is 62cm, you've determined that its angular acceleration is \(200rad/s^{2}\), the mass of the ball is \(25g\), and the instructor places the target \(190 cm\) above the launch point
Questions & Answers
QUESTION:
One day when you enter the lab, you see a spring-loaded wheel that can launch a ball straight up. To do so, you place the ball in a cup on the wheel's rim, turn the wheel to stretch the spring, then release. The wheel rotates through an angle \(\Delta\theta\), then hits a stop when the cup is level with the axle and pointing straight up. The cup stops, but the ball flies out and keeps going. You're told that the wheel has been designed to have constant angular acceleration as it rotates through \(\Delta\theta\). The lab assignment is first to measure the wheel's angular acceleration. Then the lab instructor is going to place a target at height \(h\) above the point where the ball is launched. Your task will be to launch the ball so that it just barely hits the target.
a. Find an expression in terms of quantities that you can measure for the angle \(\Delta \theta\) that launches the ball at the correct speed.
b. Evaluate \(\Delta \theta\) if the wheel's diameter is 62cm, you've determined that its angular acceleration is \(200rad/s^{2}\), the mass of the ball is \(25g\), and the instructor places the target \(190 cm\) above the launch point
ANSWER:Step 1 of 3
The ball is considered a particle. It first undergoes circular motion that we'll model as having constant angular acceleration. We'll then ignore air resistance and model the vertical motion as free fall. The free-body diagram can be drawn as follows:
