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One week in lab, you’re given a spring-loaded bar that can
Chapter 9, Problem 30P(choose chapter or problem)
Problem 30P
One week in lab, you’re given a spring-loaded bar that can be used to strike a metal ball. Your assignment is to measure what size impulse the bar delivers to the ball. You and your lab partner decide to place several balls of different mass on the edge of the lab table, use the striker to launch them horizontally, and measure the horizontal distance to where each ball hits the floor.
a. Let the table height be h and the horizontal distance traveled by the ball be its range R. Find an expression for the range. The range depends on h, the ball’s mass in, and the impulse J.
b. What should you graph the measured range against to get a linear graph whose slope is related to J?
c. After measuring the table height to be 1.5 m, you and your partner acquire the following data:
Mass (g) |
Range (cm) |
100 |
247 |
150 |
175 |
200 |
129 |
250 |
98 |
Questions & Answers
QUESTION:
Problem 30P
One week in lab, you’re given a spring-loaded bar that can be used to strike a metal ball. Your assignment is to measure what size impulse the bar delivers to the ball. You and your lab partner decide to place several balls of different mass on the edge of the lab table, use the striker to launch them horizontally, and measure the horizontal distance to where each ball hits the floor.
a. Let the table height be h and the horizontal distance traveled by the ball be its range R. Find an expression for the range. The range depends on h, the ball’s mass in, and the impulse J.
b. What should you graph the measured range against to get a linear graph whose slope is related to J?
c. After measuring the table height to be 1.5 m, you and your partner acquire the following data:
Mass (g) |
Range (cm) |
100 |
247 |
150 |
175 |
200 |
129 |
250 |
98 |
ANSWER:
Step 1 of 5
a.)
We have to find an expression for the range of the ball.
The time it takes for the ball in free fall to hit the floor can be found from the kinematic equation.
\(s_{f}=s_{i}+v_{i s}+\frac{1}{2} a_{s}(\Delta t)^{2}\)
Where,
\(s_{f}=\text { height of the table }=\mathrm{h} \text { in } \mathrm{m}\)
\(s_{i}=0 \mathrm{~m} \)
\(v_{i s}=\text { initial velocity of the }\)
\(\quad \mathrm{ball}=0 \mathrm{~m} / \mathrm{s}\)
\(a_{s}=g \mathrm{~m} / \mathrm{s}^{2}\)
Thus,
\(h=0+0+\frac{1}{2} g(\Delta t)^{2}\)
\(\Delta t=\sqrt{\frac{2 h}{g}}\)