26. How many half-lives does it take a radioactive substance to decay until only one-eighth of the original substance remains?

Question

a
two
b
three
c
eight
d
six

27. 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?

a
25 g
b
100 g
c
50 g
d
75 g

28. He’s riding his skateboard down a ramp. Assume that his acceleration is 0.8 m/s2. How much force does it take for him to accelerate at this rate? Zeke has a mass of 50 kg.

a
50 N
b
40 kg
c
62.5 N
d
40 N

29. 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

30. A block with a mass of 55 kg is pulled with a force of 220 N. Assuming a frictionless surface, what will be the acceleration of the block?

a
0.25 m/s2

b
9.8 m/s2

c
22 m/s2

d
4.0 m/s2

31.
Trial: 1, 2, 3
Force (N): 10 N, 12, 22
Acceleration (m/s^2): 2.5, 3, 5.5
Students are running an experiment in which they are measuring the acceleration after applying forces to a cart. Using the data above, what is the mass of the cart?
a
2 kg
b
4 kg
c
6 kg
d
8 kg

32. 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?

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

Answer 1

Here are the answers to each of the questions provided:

26. How many half-lives does it take a radioactive substance to decay until only one-eighth of the original substance remains?

• Answer: b (three)
• Explanation: After one half-life, 1/2 remains; after two half-lives, 1/4 remains; and after three half-lives, 1/8 remains.

27. 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?

• Answer: a (25 g)
• Explanation: After 5 days (one half-life), 50 g remains. After another 5 days (two half-lives), 25 g remains.

28. He’s riding his skateboard down a ramp. Assume that his acceleration is 0.8 m/s². How much force does it take for him to accelerate at this rate? Zeke has a mass of 50 kg.

• Answer: c (40 N)
• Calculation: Force = mass × acceleration = 50 kg × 0.8 m/s² = 40 N.

29. 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?

• Answer: 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)

30. A block with a mass of 55 kg is pulled with a force of 220 N. Assuming a frictionless surface, what will be the acceleration of the block?

• Answer: d (4.0 m/s²)
• Calculation: Acceleration = Force / mass = 220 N / 55 kg = 4.0 m/s².

31. Trial: 1, 2, 3 Force (N): 10 N, 12 N, 22 N Acceleration (m/s²): 2.5, 3, 5.5. Using the data above, what is the mass of the cart?

• Answer: a (4 kg)
• Using the second trial: Force = 12 N, Acceleration = 3 m/s².
• Calculation: Mass = Force / Acceleration = 12 N / 3 m/s² = 4 kg.

32. 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?

• Answer: c (1000 N)
• Explanation: According to Newton's Third Law, the forces are equal in magnitude and opposite in direction.

If you have any more questions or need further clarification, feel free to ask!