Question

1. Distinguish between the relationship that

Answer 1

1) $a=\frac{v-u}{t}$, $F=ma$

2) Net force is the vector sum of all forces acting on an object

3) The acceleration doubles

4) The acceleration halves

5) See definitions below

6) Newton's second law states that the net force acting on an object is equal to the product between the mass of the object and its acceleration (F=ma)

7) The force is 20 000 N

8) The force of friction is opposite to the direction of motion

9) The force applied is 100 N, the acceleration is zero, and the net force is zero

Explanation:

1)

The equation that defines acceleration is:

$a=\frac{v-u}{t}$

where

v is the final velocity

u is the initial velocity

t is the time

While the equation that states how acceleration is produced is Newton's second law of motion:

$F=ma$

where

F is the net force

m is the mass of the object

a is the acceleration

2)

The net force acting on an object is the sum of all the forces acting on the object. Since force is a vector, it is important to take into account the direction of the forces when calculating their (vector) sum.

The general procedure to calculate the net force is:

1. First, we resolve each force along two perpendicular directions, generally x- and y-
2. Then we find the x- and y- components of the net force by adding all the components along each direction
3. Then we find the net force by using Pythagorean's theorem, $F=\sqrt{F_x^2+F_y^2}$

3)

We can answer by looking at Newton's second law:

$F=ma$

which can be rewritten as

$a=\frac{F}{m}$

We see that acceleration is directly proportional to the net force: so, if the net force is doubled (F' = 2F), the new acceleration is

$a'=\frac{(2F)}{m}=2(\frac{F}{m})=2a$

4)

As before, we can rewrite the acceleration from Newton's second law:

$a=\frac{F}{m}$

We see that acceleration is inversely proportional to the mass: so, if the mass is doubled (m' = 2m), the new acceleration is

$a'=\frac{F}{(2m)}=\frac{1}{2}(\frac{F}{m})=\frac{a}{2}$

So, the acceleration halves.

5)

• Directly proportional: two variables are directly proportional if when one of the two increases, the other one increases too. An example is the acceleration and the net force in Newton's second law: as the force increases, the acceleration increases too
• Inversely proportional: two variables are inversely proportional if when one of the two increases, the other one decreases. An example is the acceleration and the mass in Newton's second law: as the mass increases, the acceleration decreases

6)

Newton's second law states that the net force acting on an object is equal to the product between the mass of the object and its acceleration.

Mathematically, it is expressed by the equation:

$F=ma$

where:

F is the net force

m is the mass

a is the acceleration

7)

In order to solve this problem, we apply Newton's second law:

$F=ma$

where in this problem, we have:

m = 20,000 kg is the mass of the rocket

$a=1 m/s^2$ is its acceleration

Substituting in the equation, we find:

$F=(20,000)(1)=20,000 N$

8)

The force of friction is caused by the roughness of the surfaces: when an object slides on a surface, the two surfaces of contact are not perfectly smooth, but they are rough; therefore, these "micro-bumps" cause a force that "resists" the motion of the object.

Therefore, the direction of the force of friction is opposite to that of the motion of the object. For a flat surface, the force of friction is given by

$F_f = \mu N$

where $\mu$ is the coefficient of friction and N the normal force on the object.

9)

Newton's second law is

$F=ma$

In this case, the net force is

$F=F_a - F_f$

where $F_a$ is the applied force and $F_f$ the  force of friction. We know that

$F_f = 100 N$

And that the object is at constant velocity, so

$a=0$

Which means that the net force is zero:

$F_a - F_f = 0\\F_a = F_f = 100 N$

So, the force applied is 100 N, the acceleration is zero, and the net force is zero.

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