1. a fully loaded rocket has a mass of 2.92x10^6kg. It's engines has a thrust of 3.34x10^7N

a)what is the downward force of gravity of the rocket at blast off?

b)what is the unbalanced force on the rocket at blast off?

c)what is the accleration of the rocket as it leaves the launching pad?

d) as the rocket travels upwards, the engine thrust remains constant but the mass of the rocket decreases. Why? (is it because the fuel is being burnt?)

e)does the acceleration of the rocket increase, decrease or remain the same as the engines continue to fire?

2. a)using Newtons laws, explain how snow tires are different from all-season radials
b)propose another use for snow tire technology

a)

m g = 2.92*10^6 * 9.81

b)
F = Thrust - m g

c)
F= m a
so
a = (Thrust-m g)/ m

d)
The rocket is losing mass of both fuel and the oxidizer for the fuel (O2 in tanks sometimes)

e)
a = Thrust/m - mg/m = Thrust/m - g
so
if thrust is constant and m decreases, a increases

2) increase friction force, particularly if studded snow tires.

winter hiking boots?

a) The downward force of gravity can be calculated by using the formula F = m*g, where F is the force of gravity, m is the mass of the rocket, and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, F = 2.92x10^6 kg * 9.8 m/s^2. But let's be honest, gravity can be a real drag, especially on a rocket trying to take off!

b) The unbalanced force on the rocket at blast off is the difference between the thrust of the engines and the force of gravity. It's like a tug of war between gravity pulling the rocket down and the engines pushing it up. Messy, right?

c) The acceleration of the rocket can be calculated using the formula a = F/m, where a is the acceleration, F is the unbalanced force, and m is the mass of the rocket. So, a = (3.34x10^7 N - F)/2.92x10^6 kg. That's one fast rocket!

d) Absolutely! The mass of the rocket decreases as the fuel is burnt. It's like going on a diet while flying through the sky! The fuel is being used up to generate the thrust needed for the rocket to overcome gravity and ascend into space. Shed those extra pounds, rocket!

e) As the engines continue to fire, the mass of the rocket decreases, but the engine thrust remains constant. Since acceleration is directly proportional to the force applied and inversely proportional to mass, the acceleration of the rocket will actually increase. It's like getting a boost of energy after shedding a few pounds. So, rocket, keep firing those engines and reach for the stars!

2. a) Newton's laws of motion can explain the difference between snow tires and all-season radials. Snow tires are specifically designed for snowy and icy conditions, with a deeper tread pattern and additional siping (small cuts) in the tread blocks. This helps increase traction and improve grip on slippery surfaces. On the other hand, all-season radials are designed to perform well in a variety of conditions, including dry, wet, and mildly snowy conditions. They have a shallower tread pattern and lesser siping, which might not provide the same level of traction as snow tires on slippery surfaces.

b) Another use for snow tire technology could be creating shoes with specialized traction for hiking or walking on icy or snowy terrains. Imagine never slipping and sliding on icy sidewalks again! You'll be walking like a penguin, but with style and grip. Safety first!

a) The downward force of gravity on the rocket can be calculated using the equation F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the mass of the rocket is given as 2.92x10^6 kg. The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Therefore, the force of gravity is:

F = (2.92x10^6 kg)(9.8 m/s^2) = 2.86x10^7 N

b) The unbalanced force on the rocket at blast off is the difference between the thrust force of the engines and the force of gravity. In this case, the thrust force is given as 3.34x10^7 N and the force of gravity is 2.86x10^7 N. Therefore, the unbalanced force is:

3.34x10^7 N - 2.86x10^7 N = 4.8x10^6 N

c) The acceleration of the rocket can be calculated using Newton's second law, which states that acceleration is equal to the net force divided by the mass of the object. In this case, the mass of the rocket is given as 2.92x10^6 kg and the unbalanced force is 4.8x10^6 N. Therefore, the acceleration is:

a = (4.8x10^6 N) / (2.92x10^6 kg) = 1.64 m/s^2

d) Yes, the mass of the rocket decreases as it travels upwards because fuel is being burnt. The burning of fuel reduces the overall mass of the rocket.

e) The acceleration of the rocket will decrease as the engines continue to fire. This is because as the mass of the rocket decreases (due to fuel burn), the same thrust force from the engines generates a larger acceleration. This can be seen from Newton's second law, as the net force remains constant while the mass decreases, resulting in an increased acceleration.

2. a) Snow tires are different from all-season radials in their tread design and composition. Snow tires typically have deeper tread patterns with wider grooves, and they are made from a softer rubber compound. This softer rubber compound offers better grip and flexibility in cold temperatures, allowing the tire to maintain traction on snowy or icy surfaces. Additionally, the deeper tread and wider grooves help to channel snow and slush away from the tire, improving traction even further.

b) Another potential use for snow tire technology could be in off-road vehicles. The tread design and composition of snow tires could provide increased traction and grip on uneven surfaces, such as dirt, gravel, or mud. Their ability to channel away debris and maintain grip in challenging conditions could be beneficial for off-road driving and exploration.

a) To find the downward force of gravity of the rocket at blast off, we can use the equation:

Force of gravity = mass * acceleration due to gravity

The mass of the rocket is given as 2.92x10^6 kg. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.

So, the downward force of gravity of the rocket at blast off would be:

Force of gravity = mass * acceleration due to gravity
= 2.92x10^6 kg * 9.8 m/s^2

b) The unbalanced force on the rocket at blast off is the difference between the thrust of the engines and the force of gravity acting on the rocket.

Unbalanced force = Thrust - Force of gravity

c) The acceleration of the rocket as it leaves the launching pad can be calculated using Newton's second law of motion:

Force = mass * acceleration

The net force acting on the rocket is the difference between the thrust and gravity. So the equation can be written as:

Thrust - Force of gravity = mass * acceleration

Rearranging the equation, we get:

Acceleration = (Thrust - Force of gravity) / mass

d) Yes, the mass of the rocket decreases as it travels upwards because the fuel is being burnt. The rocket engines burn fuel to generate thrust, and as the fuel is consumed, the total mass of the rocket reduces.

e) The acceleration of the rocket decreases as the engines continue to fire because the mass of the rocket decreases due to burning fuel. According to Newton's second law, acceleration is inversely proportional to mass. As the mass decreases, the acceleration decreases.

2. a) Snow tires are different from all-season radials in their tread design. Snow tires are specifically designed with deeper treads and specific patterns to provide better traction on snow and ice-covered roads. The deeper treads help to channel away slush and water, while the specific patterns create more edges for improved grip on slippery surfaces. All-season radials, on the other hand, have shallower treads and a different tread pattern optimized for a variety of road conditions, providing a compromise between summer and winter performance.

b) Another possible use for snow tire technology could be in off-road vehicles or vehicles used in rugged terrains. The deeper and more aggressive treads found in snow tires could provide better traction and grip on uneven or loose surfaces, such as dirt, gravel, or sand. This could enhance the vehicle's off-road capabilities and maneuverability in challenging environments.