Here are the answers to the questions provided:
Question 11: To find the mass of the second rocket, we use Newton's Second Law, F = ma. The first rocket accelerates at a rate determined by the force from the engine and its mass: \[ a_1 = \frac{F}{m_1} = \frac{100,N}{0.8,kg} = 125, m/s^2 \]
The second rocket will accelerate at half this rate: \[ a_2 = \frac{125}{2} = 62.5, m/s^2 \]
Using the same force: \[ m_2 = \frac{F}{a_2} = \frac{100,N}{62.5, m/s^2} = 1.6,kg \]
Answer: b 1.6 kg
Question 12: The half-life of element X is 5 days. After 10 days (which is two half-lives), we calculate as follows:
- After the first 5 days, 50 g remains.
- After the next 5 days, half of 50 g remains, which is 25 g.
Answer: a 25 g
Question 13: Using the data provided, we can calculate mass using F = ma for any trial. Let’s use the first trial: \[ m = \frac{F}{a} = \frac{10,N}{2.5,m/s^2} = 4,kg \]
Using a different trial (Trial 2): \[ m = \frac{12,N}{3,m/s^2} = 4,kg \]
Using Trial 3 for confirmation: \[ m = \frac{22,N}{5.5,m/s^2} = 4,kg \]
Answer: b 4 kg
Question 14: Balancing the equation \( \text{Na}_2\text{O} + \text{CaBr}_2 \rightarrow \text{NaBr} + \text{CaO} \):
- 2 Na on the left → need 2 NaBr on the right.
- 1 Ca on each side confirmed.
- 2 Br on the left → need 2 NaBr on the right.
Balanced equation: \[ 1 \text{Na}_2\text{O} + 1 \text{CaBr}_2 \rightarrow 2 \text{NaBr} + 1 \text{CaO} \]
So, the ratio is 1:1:2:1.
Answer: b 1:1:2:1
Question 15: According to Newton's Third Law, every action has an equal and opposite reaction. If the sledgehammer hits the wall with a force of 1000 N, the wall applies an equal force back on the sledgehammer.
Answer: c 1000 N
Question 16: To find the weight of an object on Mars, use the equation \( W = mg \). \[ W = 16,kg \times 3.8,m/s^2 = 60.8,N \] Rounded:
Answer: d 61 N
Question 17: During the collision between a baseball and a bat, both exert forces on each other. According to Newton's Third Law, these forces are equal in magnitude and opposite in direction.
Answer: d The force of ball on bat and the force of the bat on ball
Question 18: The applied force to the right is 25 N, while the frictional force to the left is 18 N. The net force can be determined by subtracting the friction from the applied force: \[ 25 N - 18 N = 7 N \text{ (net right)} \]
Thus, there is an unbalanced net force to the right.
Answer: b The animal will move to the right due to an unbalanced force on the right
Question 19: The phase change where a gas turns into a liquid is called condensation.
Answer: a Condensation
Question 20: It’s easier to push a heavy object that is already moving because the force of friction is generally lower on moving objects due to inertia (kinetic friction is less than static friction).
Answer: b The force of friction on the object is different if it is stationary or not