Solved Exercises of Newton's laws of motion

Solved exercises worksheet

Test what you have learned in the subject Newton's laws of motion with this list of exercises with their respective solutions and classified by sections.

Decomposition of Forces

Finding out the angled force with axis

dificulty

A force is given by the following expression: $\vec{F} = 3 \cdot \vec{i} + 2 \cdot \vec{j}$ . Calculate angle of horizontal.

Solution

Force from angle and magnitude

dificulty

Determine the analytic expression of a force knowing that it forms an 120º angle on X – axis and it has a 5 N magnitude.

Solution

Concurrent and Parallel Forces

Concurrent or parallel forces?

dificulty

Determine if they are concurrent or non concurrent forces (parallel).

Solution

Resultant Force of a System of Forces

Massive force

dificulty

If the following forces act on a body: ${\vec{F}}_{1} = - 10 \cdot \vec{i} + 10 \cdot \vec{j} ⋮ {\vec{F}}_{2} = 4 \cdot \vec{i} - 3 \cdot \vec{j} ⋮ {\vec{F}}_{3} = 5 \cdot \vec{i} - \vec{j} ⋮ {\vec{F}}_{4} = \vec{i} - \vec{j}$

Find out a force whose effect is equal to exert the 4 forces proposed.

Solution

Adittion of forces on the same direction

dificulty

Two friends, a stocky one and a slim one, push a coach on the same direction. The first one exert a force of 11 N and the second one a force of 7 N. What is the resultant force?

Solution

Addition of forces on opposite directions

dificulty

A boy and a girl tight two cords to a ring and play to find out who is stronger. The boy grab one of the cords and exert a force of 11 N, the girl applies 13 N at the same time. If both pull the cords on different directions... Who will win?

Solution

Linear Momentum

dificulty

On a given instant of time, a rocket has a velocity of $\vec{v} = 12 \cdot \vec{i} - 7 \cdot \vec{j} m / s$ . Knowing that its mass is 2kg. What is the momentum on that instant?

Solution

Linear Momentum of several particles

dificulty

Two pool balls have the following velocity:

Knowing that m₁ = 170 g y m₂ = 156 g, calculate the system´s linear momentum formed by both balls.

Solution

Newton´s Second Law

Force and trajectory

dificulty

If the equation of trajectory of a body is $\vec{r} = t^{2} \vec{i} - 5 t \vec{j} - 2 t^{2} \cdot \vec{k}$ m, What is the force that makes it move if its mass is 4kg?

Solution

Acceleration from forces

dificulty

The following forces act on a body:

${\vec{F}}_{a} = \vec{i} + \vec{j} N; {\vec{F}}_{b} = \vec{j} + \vec{k} N; {\vec{F}}_{c} = \vec{i} + \vec{k} N$

What is the acceleration of the body if its mass is 2kg?

Solution

Relationship between masses based on Newton´s second law

dificulty

Two bodies have acceleration 6 m/s² y 9 m/s² respectively, if they are under the same force. What is the relationship between masses?

Solution

Traveled distance by a body from force

dificulty

A 6kg body initially on repose experiences a force of 10 N for 4 seconds. What distance does it travel?

Solution

Newton´s second law and the nail in the wall

dificulty

Pablito is nailing a nail into the wall by using a 2kg hammer of mass. The impact speed is 6m/s. What is the resistance force of the wood if the nail is 5mm depth?

Solution

Newton´s Third Law

Newton´s third law

dificulty

Can you say what does a ball on a table interact with and where the forces are exerted at each interaction?

Solution

Impulse

dificulty

A 1kg body is subjected to a single force $\vec{F} = - 6 \cdot \vec{i} + 8 \cdot \vec{j} N$ for 5s. If we know that its initial velocity is $\vec{v_{o}} = 15 \cdot \vec{i} - 10 \cdot \vec{j} N$ . Calculate:

a)Impulse

b)Linear momentum before and after the force is exerted.

Solution

Several forces´s impulse

dificulty

A 35 kg body at rest is subjected to the following forces for 3 minutes:

${\vec{F}}_{1} = 125 \cdot \vec{i} + 200 \cdot \vec{j}; {\vec{F}}_{2} = - 400 \cdot \vec{i}; {\vec{F}}_{3} = - 150 \cdot \vec{i} + 180 \cdot \vec{j}$

If N is the measure given, calculate:

1. Resultant force

2. Impulse

3. Linear momentum variation

Velocity aquired by the body during these 3 minutes. La velocidad que ha adquirido el cuerpo in these 3 minutes.

Solution

Impulse from linear momentum variation

dificulty

A 50 g rubber ball is hit by a racket. Ball´s velocity before the hit is ${\vec{v}}_{i} = - 20 \cdot \vec{i} - 20 \vec{j} m / s$ ,after the hit, the velocity is ${\vec{v}}_{f} = 15 \cdot \vec{i} + 20 \vec{j} m / s$ .

Determine the impulse exerted by the racket on the ball and the value of the force, assumed constant, if the are in contact for 0.05 s.

Solution

Force from impulse

dificulty

Alice has had a traffic accident when she was driving at 90 km/h. Thanks she was wearing the seatbelt she survived. Can you say what average force has the seatbelt exerted if the impact last 0.05 s and Alice weights 55 kg?

Solution

Interpretation of impulse in graphs

dificulty

The following figure represents 3 different forces acting on 3 bodies of equal mass on identical conditions. Knowing that the 3 of them start on rest position, what of them will gain more final speed?

Solution

Momentum Conservation Principle

Conservation of linear momentum principle

dificulty

A competitor shoots a plate by using a rifle of 2,5 Kg on a skeet shooting competition. Knowing that the ball is 23 g and it is shot horizontally at 350 m/s, what is the recoil of the rifle?

Solution

Collision velocity and momentum conservation

dificulty

A 3 Kg ball is moving towards left at 6 m/s. It collides with a 5 Kg ball moving towards right at 2 m/s. After the collision the second ball went through the left at 3 m/s. Calculate the velocity of the first ball after the crash.

Solution

Momentum conservation in explosions

dificulty

A 10 Kg body is moving at ${\vec{v}}_{i} = \vec{i} + \vec{j} m / s$ and after its explosion it breaks into 3 pieces. The first piece is 3 Kg and goes through to ${\vec{v}}_{1} = \frac{1}{2} \cdot \vec{i} + 2 \cdot \vec{j} m / s$ , the second body weights 5 Kg and goes through to ${\vec{v}}_{2} = 2 \cdot \vec{i} + \frac{1}{2} \cdot \vec{j} m / s$ . What velocity does the third piece reach?

Solution

Momentum conservation - variable mass

dificulty

A truck moves 40 Km/hr in a straight line over a conventional road. An open container is placed on the truck. The total weight is 1800 Kg. When it starts to rain, the container got filled with water at 6 L/ min. Paying no heed to friction , what is the speed of the truck after one hour of rain?

Solution

Solved exercises worksheet

Decomposition of Forces

Finding out the angled force with axis

Force from angle and magnitude

Concurrent and Parallel Forces

Concurrent or parallel forces?

Resultant Force of a System of Forces

Massive force

Adittion of forces on the same direction

Addition of forces on opposite directions

Linear Momentum

Linear Momentum

Linear Momentum of several particles

Newton´s Second Law

Force and trajectory

Acceleration from forces

Relationship between masses based on Newton´s second law

Traveled distance by a body from force

Newton´s second law and the nail in the wall

Newton´s Third Law

Newton´s third law

Impulse

Impulse

Several forces´s impulse

Impulse from linear momentum variation

Force from impulse

Interpretation of impulse in graphs

Momentum Conservation Principle

Conservation of linear momentum principle

Collision velocity and momentum conservation

Momentum conservation in explosions

Momentum conservation - variable mass

Site

Contact form

Follow us

Dynamics

Ayúdanos a mantenernos en órbita

¿Nuestros contenidos te están resultando de utilidad?

Solved exercises worksheet

Finding out the angled force with axis

Force from angle and magnitude

Concurrent or parallel forces?

Massive force

Adittion of forces on the same direction

Addition of forces on opposite directions

Linear Momentum

Linear Momentum of several particles

Force and trajectory

Acceleration from forces

Relationship between masses based on Newton´s second law

Traveled distance by a body from force

Newton´s second law and the nail in the wall

Newton´s third law

Impulse

Several forces´s impulse

Impulse from linear momentum variation

Force from impulse

Interpretation of impulse in graphs

Conservation of linear momentum principle

Collision velocity and momentum conservation

Momentum conservation in explosions

Momentum conservation - variable mass