**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

A force is given by the following expression:

#### Force from angle and magnitude

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?

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

### Resultant Force of a System of Forces

#### Massive force

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

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

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

On a given instant of time, a rocket has a velocity of

#### Linear Momentum of several particles

Two pool balls have the following velocity:

Knowing that m_{1} = 170 g y m_{2} = 156 g, calculate the system´s linear momentum formed by both balls.

### Newton´s Second Law

#### Force and trajectory

If the equation of trajectory of a body is

#### Acceleration from forces

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

Two bodies have acceleration 6 m/s^{2} y 9 m/s^{2} respectively, if they are under the same force. What is the relationship between masses?

#### Traveled distance by a body from force

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

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

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

### Impulse

#### Impulse

A 1kg body is subjected to a single force

a)Impulse

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

#### Several forces´s impulse

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

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

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

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

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

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

A 10 Kg body is moving at

#### Momentum conservation - variable mass

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?