Question

a tractor carrying hay bales has a total mass of 9100 kg. what force is required to reach an acceleration of 4 m/s²
a cannonball accelerates at 1000 m/s² from an applied force of 5000 n. what is the mass of the cannonball?
a 1000 kg satellite in space needs a course correction. to achieve this, one of its rocket motors is fired to apply 100 n of force as thrust. what will be the acceleration due to this thrust?
how much force is needed to accelerate a 2000kg car by 3 m/s²?
a tiny aeroplane accelerates at 35 m/s² with a force of 20 n. what is the mass of the aeroplane?
what would be the acceleration of a projectile with a 6 kg mass being launched by piston force of 500 n?

Explanation:

1. For the tractor problem:

• We use Newton's second - law formula $F = ma$, where $m$ is mass and $a$ is acceleration.
• Step1: Identify the values
• Given $m = 9100$ kg and $a=4$ m/s².
• Step2: Calculate the force
• Substitute the values into the formula $F=ma$. So, $F = 9100\times4=36400$ N.

1. For the cannon - ball problem:

• Rearrange Newton's second - law formula $F = ma$ to solve for $m$, getting $m=\frac{F}{a}$.
• Step1: Identify the values
• Given $F = 5000$ N and $a = 1000$ m/s².
• Step2: Calculate the mass
• Substitute the values into the formula $m=\frac{F}{a}$. So, $m=\frac{5000}{1000}=5$ kg.

1. For the satellite problem:

• Rearrange Newton's second - law formula $F = ma$ to solve for $a$, getting $a=\frac{F}{m}$.
• Step1: Identify the values
• Given $F = 100$ N and $m = 1000$ kg.
• Step2: Calculate the acceleration
• Substitute the values into the formula $a=\frac{F}{m}$. So, $a=\frac{100}{1000}=0.1$ m/s².

1. For the car problem:

• Use Newton's second - law formula $F = ma$.
• Step1: Identify the values
• Given $m = 2000$ kg and $a = 3$ m/s².
• Step2: Calculate the force
• Substitute the values into the formula $F=ma$. So, $F=2000\times3 = 6000$ N.

1. For the aeroplane problem:

• Rearrange Newton's second - law formula $F = ma$ to solve for $m$, getting $m=\frac{F}{a}$.
• Step1: Identify the values
• Given $F = 20$ N and $a = 35$ m/s².
• Step2: Calculate the mass
• Substitute the values into the formula $m=\frac{F}{a}$. So, $m=\frac{20}{35}=\frac{4}{7}\approx0.57$ kg.

1. For the projectile problem:

• Rearrange Newton's second - law formula $F = ma$ to solve for $a$, getting $a=\frac{F}{m}$.
• Step1: Identify the values
• Given $F = 500$ N and $m = 6$ kg.
• Step2: Calculate the acceleration
• Substitute the values into the formula $a=\frac{F}{m}$. So, $a=\frac{500}{6}=\frac{250}{3}\approx83.33$ m/s².

Answer:

• Tractor force: 36400 N
• Cannon - ball mass: 5 kg
• Satellite acceleration: 0.1 m/s²
• Car force: 6000 N
• Aeroplane mass: $\frac{4}{7}$ kg
• Projectile acceleration: $\frac{250}{3}$ m/s²