Worksheet: Linear Momentum

In this worksheet, we will practice calculating the momentum of a particle moving in a straight line by using the formula H=mv.

Q1:

Determine the momentum of a car of mass 2.1 metric tons moving at 42 km/h.

Q2:

Calculate the momentum of a stone of mass 520 g after it has fallen 8.1 m vertically downward. Consider the acceleration due to gravity to be 𝑔=9.8/ms.

Q3:

A body of mass 12 g accelerated from rest at 19 cm/s2. Given that its motion was in a straight line, find its momentum 0.1 minutes after it started moving.

Q4:

Find the momentum of a body with a mass of 33 kg moving with a velocity of 18 km/h. Give your answer in gram-centimeters per second.

Q5:

A gun fires 97 bullets per minute. The mass of each bullet is 10 g, and the muzzle speed of the gun is 180 m/s where the muzzle speed is the exit speed of the bullet from the barrel of the gun. Find the momentum transferred to the bullets per second.

Q6:

A body of mass 17 kg moves in a straight line with constant acceleration of 1.8 m/s2. Its initial velocity is 22.3 m/s. Find the increase in its momentum in the first 5 seconds.

Q7:

A car was moving on a straight road at 60 km/h through a sandstorm which was moving at 48 km/h in the opposite direction. If the mass of a grain of sand in the sandstorm was 10 milligrams, determine its momentum relative to the car in gram-centimeters per second.

Q8:

Water vapor condenses on the surface of a plane in the sky and then falls in the form of drops at a rate of 14.7 kg/s. Given that the mass of one water drop is 0.39 g, determine the momentum of a water drop when it reaches the surface of the ground from a height of 1,000 m. Take 𝑔=9.8/ms.

Q9:

Find the height from which a body of mass 0.3 kg would have to fall in order for the magnitude of its momentum just before hitting the ground to be equal to the momentum of a body of mass 63 g moving at 336 km/h.

Q10:

A horizontal force of magnitude 265 kg-wt started acting on a body of mass 10 kg at rest on a horizontal plane. Given that the body started moving and that the resistance to its movement was of magnitude 2,208 N, find the momentum of the body 4 seconds after the force started acting on it. Take 𝑔=9.8/ms.

Q11:

A cannon of mass 2.7 metric tons was moving at 2 km/h in a straight line whereas the cannon ball of mass 10 kg was moving at 124 m/s. Given that the momentum of the cannon is 𝐻 and the momentum of the cannon ball is 𝐻. Which of the following statements is true?

  • A 𝐻 < 𝐻  
  • B 𝐻 > 𝐻  
  • C 𝐻 = 𝐻  

Q12:

A broken-down car of mass 1.2 metric tons was being pushed along a horizontal road. Starting from rest, a force of 240 kg-wt acted on it for 9 seconds. When the force stopped, the car continued to move freely. It came to rest again 19 seconds later. The resistance to the car’s motion was constant throughout its movement. Using the relationship between impulse and momentum, find the maximum speed the car reached. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A25.27 m/s
  • B17.06 m/s
  • C3.87 m/s
  • D11.97 m/s

Q13:

A tennis ball of mass 57 g was moving horizontally at 68.4 m/s when it collided with a vertical racket that was at rest, after which it rebounded at 18.8 m/s. Given that the contact time between the ball and racket was 125 of a second, find the magnitude of the average impact force.

Q14:

A machine gun fires 840 bullets per minute at a steel wall. Each bullet has a mass of 24.5 g and its speed when it hits the wall is 120 m/s. Find the force acting on the wall given that each bullet rebounds at 30 m/s. Take 𝑔=9.8/ms.

Q15:

A rubber ball fell from a height of 7.2 m. When it hit the ground, it bounced back to a height of 2.7 m. Find the velocity of the ball as it rebounded from the ground. Take the acceleration due to gravity 𝑔=9.8/ms.

  • A 2 1 √ 6 2 0 m/s
  • B 2 1 √ 3 1 0 m/s
  • C 2 1 √ 6 1 0 m/s
  • D 2 1 √ 3 5 m/s

Q16:

A boy was practicing kick-ups. Given that the ball took 2.6 seconds to return to his foot after he kicked it and that 𝑔=9.8/ms, determine the velocity of the ball just after he kicked it.

Q17:

Oil was flowing continuously from a height of 122.5 cm into the pan of a scale balance at a rate of 480 g/min. Given that the oil was gathering in the pan without rebounding, find the reading on the balance 20 seconds after the oil started flowing. Take 𝑔=9.8/ms.

Q18:

A bullet of mass 16 g was fired horizontally. A constant force of 128 N acted on the bullet for the 0.05 s it took for the bullet to travel down the barrel of the gun. What was the speed of the bullet as it left the gun’s barrel?

Q19:

A car of mass 1.6 metric tons, starting from rest, began accelerating uniformly at 137 cm/s2. Find its momentum 19 seconds after it started moving.

Q20:

A body of mass 7 kg is moving in a straight line. Its position vector at a time 𝑑 is given by the relation rij(𝑑)=𝑑+5+𝑑+π‘‘ο…οŠ¨οŠ©, where ||r is measured in meters and 𝑑 in seconds. Determine the body’s momentum after 2 seconds.

  • A 2 8 + 9 1 i j
  • B 1 4 + 1 3 i j
  • C 2 8 + 8 5 i j
  • D 5 6 + 8 4 i j

Q21:

A bullet of mass 188 g was fired at 797 m/s into a wooden target of mass 3 kg which was at rest. The bullet embedded into the target, and they started to move together. Find the speed of the bullet and target after the impact, given that the total momentum of the system did not change.

Q22:

A body of variable mass is moving along a fixed straight line. Its mass at time 𝑑 is given by the relation π‘š(𝑑)=5𝑑+7 and its displacement is given by the relation si(𝑑)=(5𝑑+4𝑑), where i is a unit vector parallel to the direction of its motion. Determine the body’s momentum H(𝑑) and the force that is acting on it F(𝑑).

  • A H i ( 𝑑 ) = ( 2 5 𝑑 + 5 5 𝑑 + 2 8 )  , F i ( 𝑑 ) = ( 5 0 𝑑 + 5 5 )
  • B H i ( 𝑑 ) = ( 5 0 𝑑 + 9 0 𝑑 + 2 8 )  , F i ( 𝑑 ) = ( 1 0 0 𝑑 + 9 0 )
  • C H i ( 𝑑 ) = ( 5 0 𝑑 + 7 0 𝑑 + 2 8 )  , F i ( 𝑑 ) = ( 1 0 0 𝑑 + 7 0 )
  • D H i ( 𝑑 ) = ( 5 0 𝑑 + 9 0 𝑑 + 2 8 )  , F i ( 𝑑 ) = ( 5 0 𝑑 + 7 0 )

Q23:

A rocket was ascending vertically, projecting its burnt fuel at 3,600 km/h vertically downward. Given that, for every 8 seconds, it expelled 3 kg of fuel, find the elevator force generated by the rocket’s engine.

Q24:

Determine the mass of a body whose momentum is 37 kgβ‹…m/s, given that its displacement vector is given by the relation sij(𝑑)=(βˆ’3𝑑)+(4𝑑), where ||s is measured in meters and 𝑑 in seconds.

Q25:

A car of mass 1,350 kg moves in a straight line such that at time 𝑑 seconds, its displacement from a fixed point on the line is given by 𝑠=ο€Ή6π‘‘βˆ’3𝑑+4ο…οŠ¨m. Find the magnitude of the car’s momentum at 𝑑=3s.

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