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 your questions:

26. How many half-lives does it take a radioactive substance to decay until only one-eighth of the original substance remains?
    B) three
    Explanation: After one half-life, 1/2 remains; after two, 1/4 remains; after three, 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?
    A) 25 g
    Explanation: After 5 days (1 half-life), 50 g remains; after another 5 days (2 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.
    C) 40 N
    Explanation: F = m * a = 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?
    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
    Explanation: This describes inertia (Newton's First Law) since your upper body continues moving while your foot is stopped.

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?
    D) 4.0 m/s²
    Explanation: F = m * a, thus a = F/m = 220 N / 55 kg = 4.0 m/s².

31. Using the data above, what is the mass of the cart?
    D) 8 kg
    Explanation: Using the second trial (12 N, 3 m/s²), mass = F/a = 12 N / 3 m/s² = 4 kg; from the first trial (10 N, 2.5 m/s²), mass = 10 N / 2.5 m/s² = 4 kg; from the third trial (22 N, 5.5 m/s²), mass = 22 N / 5.5 m/s² = 4 kg. This confirms the mass is consistent - 4 kg for all trials.

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?
    C) 1000 N
    Explanation: Newton's Third Law states that for every action, there is an equal and opposite reaction, so the wall exerts a force of 1000 N back on the sledgehammer.