14. The half-life for a 100-gram sample of radioactive element X is 5 days. How much of element X remains after 10 days have passed?

Question

A) 25 g
B) 50 g
C) 75 g
D) 100 g

15. Which of the following would be an example of Newton's Third Law forces?

a
A horse pulling a horse cart
b
A hammer striking a nail
c
A soccer ball bouncing off a wall
d
All of the above

16. According to Newton's Third Law, if a sledgehammer hits a wall with a force of 1000 N, how much force does the wall hit the sledgehammer IF the sledgehammer does not go through the wall?

a
0 N
b
500 N
c
1000 N
d
- 1000 N

17. As you are walking, you foot gets caught on an uneven piece of sidewalk and you trip and fall. Which of the following explains what is happening using Newton's Laws?
a
The sidewalk pushed you, causing a rapid force that made you fall
b
The sidewalk provided a force to stop your foot, but the top of your body was still moving which is what causes you to tip over
c
Your foot hit the sidewalk and provided a force on it, so the sidewalk will provide another force back on your foot, equal in magnitude but opposite in direct
d
Your foot pushes the sidewalk with such force that it causes the next piece of sidewalk to be uprooted, which makes your next step miss your footing

Answer 1

Let's solve the problems one by one.

Question 14: The half-life for a 100-gram sample of radioactive element X is 5 days. How much of element X remains after 10 days have passed?

After each half-life, the amount of element X is halved.

• After 5 days (1 half-life), the amount of element X remaining = 100 g / 2 = 50 g.
• After another 5 days (2 half-lives), the amount of element X remaining = 50 g / 2 = 25 g.

Thus, after 10 days, 25 grams of element X remain. The correct answer is A) 25 g.

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Question 15: Which of the following would be an example of Newton's Third Law forces?

Newton's Third Law states that for every action, there is an equal and opposite reaction. Let’s analyze the options:

• a) A horse pulling a horse cart involves the horse pulling forward and the cart pulling back with equal force.
• b) A hammer striking a nail demonstrates that the hammer applies force on the nail, and the nail exerts an equal and opposite force on the hammer.
• c) A soccer ball bouncing off a wall involves the ball colliding with the wall and then bouncing back, indicating equal and opposite forces.

Since all these scenarios demonstrate Newton's Third Law, the correct answer is d) All of the above.

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Question 16: According to Newton's Third Law, if a sledgehammer hits a wall with a force of 1000 N, how much force does the wall hit the sledgehammer IF the sledgehammer does not go through the wall?

According to Newton's Third Law, the wall exerts an equal and opposite force back on the sledgehammer. Therefore, if the sledgehammer hits the wall with a force of 1000 N, the wall exerts a force of 1000 N back on the sledgehammer. Thus, the correct answer is c) 1000 N.

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Question 17: As you are walking, your foot gets caught on an uneven piece of sidewalk and you trip and fall. Which of the following explains what is happening using Newton's Laws?

In this context, the uneven sidewalk stops your foot suddenly (providing an upward force), while the upper part of your body continues to move forward due to inertia (Newton's First Law). Therefore, option b) The sidewalk provided a force to stop your foot, but the top of your body was still moving which is what causes you to tip over correctly explains the situation.

To summarize: 14. A) 25 g 15. d) All of the above 16. c) 1000 N 17. b) The sidewalk provided a force to stop your foot, but the top of your body was still moving which is what causes you to tip over.