Worksheet: Newton's First Law of Motion

In this worksheet, we will practice solving problems using Newton's first law.

Q1:

In the given figure, the body is at rest under the action of a system of forces. Given that the forces are measured in newtons, find the magnitudes of 𝐹 and 𝐾.

  • A 𝐹 = 1 2 3 N , 𝐾 = 2 7 N
  • B 𝐹 = 2 7 N , 𝐾 = 1 2 3 N
  • C 𝐹 = 5 7 N , 𝐾 = 9 3 N
  • D 𝐹 = 9 3 N , 𝐾 = 5 7 N

Q2:

A car of mass 1.8 metric tons is moving at a constant speed on a horizontal road. If the resistance to the motion is 57.6 kg-wt per tonne of the car’s mass, find the force of its motor.

Q3:

A body was moving uniformly under the effect of three forces F, F, and F. Given that Fi=7 and Fj=8, where i and j are orthogonal unit vectors, determine F which ensures that it will move at a constant velocity.

  • A 7 + 8 i j
  • B βˆ’ 7 βˆ’ 8 i j
  • C 7 βˆ’ 8 i j
  • D βˆ’ 7 + 8 i j
  • E 8 + 7 i j

Q4:

A body was descending vertically in a liquid such that it was covering equal distances in each consecutive time interval of equal length. Given that the weight of the body was 55 kg-wt, find the magnitude of the resistive force of the liquid acting against the motion of the body.

Q5:

In the figure, the body is moving at a constant velocity 𝑣 under the action of a system of forces. Given that the forces are measured in newtons, find the magnitudes of 𝐹 and 𝐾.

  • A 𝐹 = 5 1 N , 𝐾 = 7 9 N
  • B 𝐹 = 7 9 N , 𝐾 = 5 1 N
  • C 𝐹 = 1 1 N , 𝐾 = 7 9 N
  • D 𝐹 = 9 9 N , 𝐾 = 3 1 N

Q6:

In the given figure, the body is subject to the action of a system of forces. Given that it is moving at a constant speed 𝑣 and that the forces are measured in newtons, find 𝐹 and 𝐾.

  • A 𝐹 = 3 3 N , 𝐾 = 7 N
  • B 𝐹 = 2 N , 𝐾 = 7 N
  • C 𝐹 = 4 N , 𝐾 = 7 N
  • D 𝐹 = 4 N , 𝐾 = 5 6 N

Q7:

Two forces F and F are acting on a body of mass 2 kg on a horizontal plane. The forces are given by Fij=9βˆ’10kg-wt and Fij=2+5kg-wt where i and j are unit vectors. One of them is a direction in the horizontal plane, and the other is the upward perpendicular direction to that plane. Determine the normal reaction of the plane N and the resistance force vector R, given that the body is moving at a uniform velocity.

  • A N j = βˆ’ 7 k g - w t , R i = 7 k g - w t
  • B N j = 5 k g - w t , R i = 1 1 k g - w t
  • C N j = βˆ’ 1 3 k g - w t , R i = βˆ’ 9 k g - w t
  • D N j = 7 k g - w t , R i = βˆ’ 1 1 k g - w t

Q8:

A body weighing π‘Š is placed on a plane inclined at an angle πœƒ to the horizontal, where tanπœƒ=512. A force Fij=(29+5)N is acting on the body, where i and j are two perpendicular unit vectors where i is in the direction of the line of greatest slope up the plane, and j is the upward perpendicular to i. Given that the action of this force makes the body move uniformly up the plane against its resistive force of 9 N, find the weight of the body π‘Š and the normal reaction of the plane R.

  • A π‘Š = 7 5 . 4 N , R j = 6 4 . 6 N
  • B π‘Š = 5 2 N , R j = 4 3 N
  • C π‘Š = 2 0 N , R j = 5 N
  • D π‘Š = 2 1 . 6 7 N , R j = 1 5 N

Q9:

A particle of mass π‘š moves under the effect of the two forces Fij=βˆ’8βˆ’4 and Fij=2βˆ’8, where i and j are two perpendicular unit vectors. Find the additional force F needed to act on the particle to make it move uniformly.

  • A F i j  = 6 + 1 2
  • B F i j  = 1 2 + 6
  • C F i j  = 2 βˆ’ 4
  • D F i j  = βˆ’ 1 0 βˆ’ 4

Q10:

A body is moving in a straight line at a constant velocity under the action of a system of forces F, F, and F. If Fijk=π‘Žβˆ’βˆ’5, Fijk=βˆ’4+π‘βˆ’3, and Fijk=+6+𝑐, find π‘Ž, 𝑏, and 𝑐.

  • A π‘Ž = 3 , 𝑏 = βˆ’ 5 , 𝑐 = 8
  • B π‘Ž = 3 , 𝑏 = 7 , 𝑐 = βˆ’ 8
  • C π‘Ž = βˆ’ 3 , 𝑏 = 5 , 𝑐 = βˆ’ 8
  • D π‘Ž = 5 , 𝑏 = 7 , 𝑐 = βˆ’ 2

Q11:

A car of mass 1.5 metric tons was moving along a straight horizontal road. When the car was moving at 78 km/h, the resistance to the car’s movement was 90 kg-wt for each tonne of the car’s mass. Given that the resistance to the car’s motion is directly proportional to the magnitude of the car’s speed and that the maximum force that can be generated by its motor is 360 kg-wt, find the maximum speed of the car on this road.

Q12:

A train of mass 50 metric tons has an engine whose maximum driving force is 9,000 kg-wt. Given that the resistance to its motion due to friction is directly proportional to the square of its speed and that this resistance was 20 kg-wt for each tonne of the train’s mass when its speed was 75 km/h, find the maximum speed of the train.

Q13:

A soldier jumped out of a plane with a parachute. After he had opened his parachute, the resistance to his movement was directly proportional to the cube of his speed. When his speed was 19 km/h, the resistance to his motion was 127 of the combined weight of him and his parachute. Determine the maximum speed of his descent.

Q14:

When its engine supplies a force of 506 kg-wt, a car of mass 912 kg moves with constant velocity up a hill of inclination πœƒ. If the total resistance to the car’s motion is 16 of its weight, what is the angle of inclination, πœƒ? Give your answer to the nearest minute.

  • A 6 7 1 0 β€² ∘
  • B 4 6 1 1 β€² ∘
  • C 3 3 4 2 β€² ∘
  • D 2 2 5 0 β€² ∘

Q15:

The mass of a locomotive was 57 metric tons and the force of its engine was 1β€Žβ€‰β€Ž755 kg-wt. A number of carriages were attached to the locomotive, and then the whole train descended a section of track inclined to the horizontal at an angle whose sine is 1100. Given that the mass of each carriage is 6 metric tons, the resistance to the train’s motion was 25 kg-wt per tonne of its mass, and that it descended at a constant speed, determine the number of carriages attached to the locomotive.

Q16:

When a man was skydiving, the air resistance was directly proportional to the square of his velocity. When his velocity was 37.5 km/h, the resistance to his motion was 2516 of the combined weight of him and his parachute. Determine his terminal velocity (the maximum velocity of his descent).

Q17:

A body of mass 20 kg is pulled along a horizontal plane by a rope that makes an angle πœƒ with the plane, where tanπœƒ=512. When the tension in the rope is 91 N, the body moves with uniform velocity. Find the total resistance to the motion, 𝐹, and the normal reaction, 𝑅. Use 𝑔=9.8/ms.

  • A 𝐹 = 8 4 N , 𝑅 = 2 0 N
  • B 𝐹 = 8 4 N , 𝑅 = 1 6 1 N
  • C 𝐹 = 9 1 N , 𝑅 = 1 1 2 N
  • D 𝐹 = 3 5 N , 𝑅 = 1 1 2 N

Q18:

A body of mass 20 kg was being pulled up a plane inclined at an angle πœƒ to the horizontal by a force of magnitude 245 N which was acting up the line of greatest slope of the plane. As a result, the body was moving up the plane at a constant speed against a resistive force 𝑅. When the force was reduced to 39.2 N, the body moved down the plane at a constant speed. Given that the resistance of the plane to the body’s motion did not change, determine the angle πœƒ to the nearest minute. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 6 8 4 5 β€² ∘
  • B 2 1 1 5 β€² ∘
  • C 4 3 3 2 β€² ∘
  • D 4 6 2 8 β€² ∘

Q19:

A body of mass 8 kg was being dragged across a horizontal surface by two strings. The two strings were making an angle of 90∘ with each other, and the tension in each string was 320 g-wt. Given that the body was moving uniformly, find the magnitude and direction of the plane’s resistance to its motion, denoted by π‘Ÿ and πœƒ, respectively.

  • A 1 6 0 √ 2 g-wt, 1 3 5 ∘
  • B 3 2 0 √ 2 g-wt, 1 3 5 ∘
  • C 320 g-wt, 1 3 5 ∘
  • D 320 g-wt, 4 5 ∘
  • E 3 2 0 √ 2 g-wt, 4 5 ∘

Q20:

A truck of mass 2.8 metric tons was loaded with 1.5 metric tons of stones and descended a road inclined at an angle πœƒ to the horizontal, where sinπœƒ=1100. If the force generated by the engine of the car is 86 kg-wt and it was traveling at a constant speed, find the resistance 𝑅 to its motion per metric ton of its mass. After the car had emptied the load, it went back up the slope driving at a constant speed. Given that the resistance per metric ton of its mass on its ascent was the same as that on its descent, find the force 𝐹 generated by the engine.

  • A 𝑅 = 1 2 9 k g - w t per metric ton, 𝐹=157kg-wt
  • B 𝑅 = 3 0 k g - w t per metric ton, 𝐹=112kg-wt
  • C 𝑅 = 3 0 k g - w t per metric ton, 𝐹=58kg-wt
  • D 𝑅 = 4 0 . 7 1 k g - w t per metric ton, 𝐹=73kg-wt
  • E 𝑅 = 2 6 . 5 1 k g - w t per metric ton, 𝐹=58kg-wt

Q21:

A body of mass 1.3 kg was placed on a smooth plane inclined at 60∘ to the horizontal. A force of 62 N was acting on the body along the line of greatest slope of the plane in the upward direction. Find the magnitude of the reaction of the plane. Take 𝑔=9.8/ms.

Q22:

A train of mass 120 metric tons ascended a section of track inclined to the horizontal at an angle whose sine is 3160 at its maximum speed of 18 km/h. When it reached the top, it moved along a section of horizontal track. The resistance to the motion of the train on each section of track was directly proportional to the speed of the train. Given that the power of the engine was 200 hp, find the magnitude of the resistance 𝑅 on the horizontal track and the train’s maximum speed 𝑣 on the same section of track.

  • A 𝑅 = 3 , 0 0 0 k g - w t , 𝑣 = 1 8 / k m h
  • B 𝑅 = 1 , 5 0 0 k g - w t , 𝑣 = 3 6 / k m h
  • C 𝑅 = 1 , 5 0 0 k g - w t , 𝑣 = 1 0 / k m h
  • D 𝑅 = 7 5 0 k g - w t , 𝑣 = 3 6 / k m h

Q23:

A body is moving in a straight line under the action of three forces Fik=βˆ’9βˆ’9, Fijk=βˆ’9+βˆ’10, and F such that its displacement vector s is given as a function of time by the relation sijk(𝑑)=9𝑑+7βˆ’9𝑑. Given that s is measured in meters, and 𝑑 is measured in seconds, and the forces are measured in newtons, find the magnitude of F.

  • A36 N
  • B √ 3 8 N
  • C 7 √ 1 4 N
  • D 2 √ 1 9 N

Q24:

A body is moving under the effect of two forces F and F such that Fij=βˆ’4+6 and Fi=βˆ’2, where i and j are orthogonal unit vectors. If a third force acts on the body causing it to move uniformly, determine its magnitude.

  • A 2 √ 1 0 force units
  • B 6 √ 2 force units
  • C8 force units
  • D 4 √ 2 force units

Q25:

A car can ascend a certain hill at 63 km/h, whereas if it descends the same hill, it can reach a speed of 77 km/h. Given that the power of the car’s engine and the resistance to its motion are constant, determine the car’s top speed on a section of horizontal road.

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