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Calculating Force Based On Newton's Second Law Of Motion (1)

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From Newton's second law of motion, we have established that the force that acts on a body can be calculated by using the formula:

F = ma

Where F stands for force; m for the mass of the body, and a the acceleration of the body.

From the formula for force above, to calculate the force that acts on a body, we simply multiply its mass, which is measured in kilogram (kg) with its acceleration measured in metre per second squared (ms-2).

The acceleration of a body is the rate of change in its velocity. Stating it in mathematical term:

Acceleration (a) = v/t.

The symbol is called delta, and it represents a change in the value of a property.  v therefore stands for a change in velocity.

v = displacement / time

Therefore, acceleration = displacement/t2 and this is why the SI unit of acceleration is metres per second squared.

Hence, another way of stating the formula for force is:

Force = mass x displacement/time2

The SI unit of force is the Newton (N). This means that after you have calculated the quantity of force on a body, you must express it in Newtons.

Remember that in physics calculations, all quantities are expressed in their respective units.

Question 1.

Calculate the magnitude of an external force which acts on a particle of mass 0.15kg for 0.03s and changes its speed by 20m/s.

Solution:

Given:

Mass of particle = 0.15kg, change of velocity (v) = 20ms-1, time of change of velocity = 0.03s

Using the formula for force,

F = m x V/t

F = 0.15 x 20/0.03

F = 5 x 20 = 100N

The magnitude of the force which acted on the particle is 100 Newtons.

Question 2.

A ball of mass 0.1kg approaching a tennis player with a velocity of 10ms-1, is hit back in the direction opposite with a velocity of 15ms-1. If the time of impact between the racket and the ball is 0.01s, calculate the magnitude of the force with which the ball is hit.

Solution:

Given:

Change in velocity (v = v - u), where v is the final velocity, i.e. the velocity the ball was hit back, and u is the initial velocity, i.e. the velocity with which the ball was approaching the player.

Therefore,

change in velocity, v = 15ms-1 - 10ms-1 = 5ms-1

Mass = 0.1kg, time of change of velocity = 0.01s.

Using the formula for force,

F = m x V/t

F = 0.1 x 5/0.01

F = 50N

The magnitude of the force with which the ball is hit is 50 Newtons.

Question 3.

A body of mass 20kg is set in motion by two forces 3N and 4N, acting at right angles to each other. Determine the magnitude of its acceleration.

Solution:

Since we have two forces acting on the body at right angles to each other, we first have to resolve them to determine the magnitude of the force that actually moves the body. This we can do using a right angled triangle.

x represents the net force, which actually moves the body.

Using Pythagora's theorem, we have

x2 = 32 + 42

x2 = 9 + 16

x2 = 25

x = 5

Therefore, net force equals 5 Newtons.

Now to calculate the magnitude of its acceleration:

Using the formula for force,

F = ma

where force is 5N and mass 20kg

therefore,

5 = 20 x a

a = 5/20 = 0.25

The magnitude of the body's acceleration is 0.25 m/s2

Question 4.

A net force of magnitude 0.6N acts on a body of mass 40g, initially at rest. Calculate the magnitude of the resulting acceleration.

Solution:

Given:

Magnitude of force that acts on the body = 0.6 Newtons, mass of body = 40g. The SI unit of mass is kilogram, therefore converting mass in gram to kilogram by dividing 40g by 1000 gives the mass of body in kilogram = 0.04kg.

Using the formula for force,

F = ma

0.6 = 0.04 x a

a = 0.6/0.04 = 15

The resulting acceleration is 15m/s2

Question 5.

A bullet of mass 120g is fired horizontally into a fixed wooden block with a speed of 20ms-1. The bullet is brought to rest in the block in 0.1s by a constant resistance. Calculate the: (i) magnitude of the resistance (ii) distance, moved by the bullet in the wood.

Solution:

Note: the resistance is the force which acted on the bullet and brought it to rest (or to a complete stop). A resistance is a force, however, it does not cause an object to move, but to slow it down or to stop it completely.

When an object is brought to rest, it means it has been stopped completely - no more movement. And that means that its final velocity is zero.

Mass of bullet 0.12kg (converting 120g to kilogram, initial velocity = 20ms-1, final velocity = 0, time of change of velocity = 0.1s.

v = final velocity (zero) - initial velocity

final velocity = 0 because the bullet was brought to rest.

Therefore, v = 20ms-1

(i) Using the formula for force, F = m x V/t

F = 0.12 x 20/0.1 = 24N

The resistance is 24N

(ii) To find the distance moved by the bullet in the wood, we can use one of the equations of motion,

S = (v+u)/2 x t

Where S = distance moved by the bullet, v = final velocity, u = initial velocity,     t = time.

S = (0 + 20) / 2 x 0.1

S = 1m

Therefore, distance moved by the bullet in the wood = 1m

See more calculations based on Newton's second law of motion.