A model rocket has a mass of 0.2 kg, with a motor that can provide a force of 100 N. A second model rocket is being built with the same motor, but it is being designed to accelerate half as much as the first rocket. What kind of change can be made in the design to achieve this objective? Responses

Question

The mass of the second rocket should be 0.01 kg.

The mass of the second rocket should be 0.1 kg.

The mass of the second rocket should be 0.4 kg.

The mass of the second rocket should be 0.2 kg.

Answer 1

To determine what the mass of the second rocket should be to achieve half the acceleration of the first rocket, we can use Newton's second law, which states \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.

For the first rocket:

• Mass (\( m_1 \)) = 0.2 kg
• Force (\( F \)) = 100 N

We can calculate the acceleration of the first rocket: \[ a_1 = \frac{F}{m_1} = \frac{100 , \text{N}}{0.2 , \text{kg}} = 500 , \text{m/s}^2 \]

For the second rocket, we want the acceleration to be half of the first rocket's acceleration: \[ a_2 = \frac{a_1}{2} = \frac{500 , \text{m/s}^2}{2} = 250 , \text{m/s}^2 \]

Using the same force (100 N) for the second rocket, we can find the required mass (\( m_2 \)) to achieve this new acceleration: \[ F = m_2 \cdot a_2 \Rightarrow m_2 = \frac{F}{a_2} = \frac{100 , \text{N}}{250 , \text{m/s}^2} = 0.4 , \text{kg} \]

Thus, to achieve half the acceleration of the first rocket, the mass of the second rocket should be 0.4 kg.

The correct response is: The mass of the second rocket should be 0.4 kg.

Answer 2

Five motorboats are being tested to see which reaches the highest velocity in the same amount of time. After graphing the acceleration versus force for each motorboat, the graph is a sloped line with a y-intercept of zero. Which statement is correct about these motorboats?
Responses

All five motorboats have the same final velocity, which cannot be calculated from the graph.

All five motorboats have the same mass, which cannot be calculated from the graph.

All five motorboats have the same final velocity, which can be calculated from the graph.

All five motorboats have the same mass, which can be calculated from the graph.

Answer 3

Given that the graph of acceleration versus force for the five motorboats shows a sloped line with a y-intercept of zero, we can analyze what this indicates.

From Newton's second law, we know that: \[ F = ma \] This means that the acceleration (\(a\)) of an object is directly proportional to the force (\(F\)) applied to it when mass (\(m\)) is constant.

In the context of the graph:

• A sloped line with a y-intercept of zero indicates that acceleration increases linearly with increasing force.
• The slope of this line represents the mass (\(m\)) of the motorboats, calculated as \(m = \frac{F}{a}\).
• If the lines for all motorboats follow this relationship (a straight line passing through the origin), it suggests that they all have the same mass since the slope (which represents mass) is constant across all boats.

Thus, the correct statement is: All five motorboats have the same mass, which can be calculated from the graph.

Answer 4

If a soccer ball’s mass is 5 kg and a player who weighs 50 kg kicks the soccer ball forward with a force of 5 N , how much force does the ball exert on the player’s foot and in what direction?

100 kg forward

10 kg/N backward

5 N forward

5 N backward

Answer 5

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that when a player exerts a force on the soccer ball, the soccer ball exerts an equal force in the opposite direction back onto the player's foot.

In this case:

• The player exerts a force of 5 N forward on the soccer ball.

By Newton's third law, the soccer ball will exert a force of 5 N backward on the player's foot.

Thus, the correct response is: 5 N backward.

Answer 6

A toy helicopter flies forward with a force of 15 N into an oncoming wind of 10 N. The force of gravity pulls the helicopter down with a force of 5 N, but the propeller is providing an upward force of 10 N.

Which of the following accurately describes the helicopter’s force?

Responses:

The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.

The toy helicopter is flying forward with a force of 15 N.

The toy helicopter is flying forward with a force of 10 N and upward with a force of 5 N.

The toy helicopter is flying forward with a force of 15 N and upward with a force of 10 N.

Answer 7

To analyze the forces acting on the toy helicopter, we can break down its motion based on the information provided:

1. Forward Force: The helicopter flies forward with a force of 15 N, but it encounters an oncoming wind that applies a force of 10 N in the opposite direction.

   • The net forward force can be calculated as: \[ \text{Net Forward Force} = \text{Forward Force} - \text{Wind Force} = 15 , \text{N} - 10 , \text{N} = 5 , \text{N} \]

2. Vertical Forces: The force of gravity pulls the helicopter down with a force of 5 N, while the propeller provides an upward force of 10 N.

   • The net upward force can be calculated as: \[ \text{Net Upward Force} = \text{Upward Force} - \text{Gravity Force} = 10 , \text{N} - 5 , \text{N} = 5 , \text{N} \]

Based on the calculations:

• The net forward force is 5 N.
• The net upward force is 5 N.

Thus, the statement that accurately describes the helicopter’s force is: The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.

Answer 8

In 1-2 sentences, summarize why the force required to move a ping pong ball is less than the force required to move a bowling ball.

Answer 9

The force required to move a ping pong ball is less than that for a bowling ball due to the significant difference in their masses and inertia; the ping pong ball's much lower mass means it requires less force to accelerate according to Newton's second law (\(F = ma\)). Additionally, the bowling ball's greater mass results in higher inertia, requiring more force to achieve the same acceleration.

Answer 10

In 1-2 sentences, explain the difference between the velocity and acceleration of an object.

Answer 11

Velocity is a vector quantity that describes the speed and direction of an object's motion, indicating how fast and in which direction the object is moving. Acceleration, on the other hand, is also a vector quantity that measures the rate of change of an object's velocity over time, indicating how quickly the object’s speed or direction is changing.