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: F=3·i+2·j. Calculate angle of horizontal.

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:F1=-10·i+10·j   F2=4·i-3·j  F3 =5·i- j  F4 = i - j

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  v=12 · i - 7 · j m/s. Knowing that its mass is 2kg. What is the momentum on that instant?

Linear Momentum of several particles


Two pool balls have the following velocity:

velocity vector of two pool balls

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


If the equation of trajectory of a body is r=t2i-5 t j - 2t2 · k m, What is the force that makes it move if its mass is 4kg?

Acceleration from forces


The following forces act on a body:

Fa=i+j N ; Fb=j+k N ; Fc =i+k N 

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/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


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?




A 1kg body is subjected to a single force F=-6 ·i +8·j N for 5s. If we know that its initial velocity is vo=15 ·i -10·j N. Calculate:


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:

F1=125·i+200·j;F2=-400·i ;F3=-150·i+180·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.

Impulse from linear momentum variation


A 50 g rubber ball is hit by a racket. Ball´s velocity before the hit is vi=-20·i-20j m/s,after the hit, the velocity is vf=15·i+20j 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.

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 vi=i+j m/s and after its explosion it breaks into 3 pieces. The first piece is 3 Kg and goes through to v1=12·i+2·j m/s, the second body weights 5 Kg and goes through to v2=2·i+12·j m/s. What velocity does the third piece reach?

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?