## 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: $\stackrel{\to }{F}=3·\stackrel{\to }{i}+2·\stackrel{\to }{j}$. Calculate angle of horizontal.

#### 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.

### Concurrent and Parallel Forces

#### Concurrent or parallel forces?

dificulty

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

### Resultant Force of a System of Forces

#### Massive force

dificulty

If the following forces act on a body:

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

#### 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?

#### 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?

### Linear Momentum

#### Linear Momentum

dificulty

On a given instant of time, a rocket has a velocity of  . Knowing that its mass is 2kg. What is the momentum on that instant?

#### 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.

### Newton´s Second Law

#### Force and trajectory

dificulty

If the equation of trajectory of a body is  m, What is the force that makes it move if its mass is 4kg?

#### Acceleration from forces

dificulty

The following forces act on a body:

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

#### 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?

#### 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?

#### 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?

### 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?

### Impulse

#### Impulse

dificulty

A 1kg body is subjected to a single force  for 5s. If we know that its initial velocity is . Calculate:

a)Impulse

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

#### Several forces´s impulse

dificulty

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

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.

#### Impulse from linear momentum variation

dificulty

A 50 g rubber ball is hit by a racket. Ball´s velocity before the hit is ,after the hit, the velocity is .

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.

#### 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?

#### 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?

### 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?

#### 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.

#### Momentum conservation in explosions

dificulty

A 10 Kg body is moving at and after its explosion it breaks into 3 pieces. The first piece is 3 Kg and goes through to , the second body weights 5 Kg and goes through to . What velocity does the third piece reach?

#### 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?