Worksheet: Resultant Force

In this worksheet, we will practice calculating the sum of multiple forces with arbitrary directions and calculating the acceleration produced by such forces.

Q1:

Find the acceleration of the object of mass 5.0 kg shown in the accompanying diagram.

  • A ( 1 . 6 0 . 8 ) i j m/s2
  • B ( 1 . 6 1 . 4 ) i j m/s2
  • C ( 1 . 8 0 . 6 ) i j m/s2
  • D ( 1 . 8 1 . 6 ) i j m/s2
  • E ( 1 . 4 0 . 6 ) i j m/s2

Q2:

An object with a mass of 5.0 kg accelerates at a rate of 2.0 m/s2 in the positive 𝑥 -direction when two forces are applied to it. One of the forces acts in the positive 𝑦 -direction with magnitude 12.0 N. Find the magnitude of the other force.

Q3:

The body shown being acted on by three forces has a mass of 10.0 kg. Find the acceleration of the body.

  • A ( 0 . 4 1 7 + 1 . 1 3 ) i j m/s2
  • B ( 0 . 5 0 1 + 0 . 8 8 2 ) i j m/s2
  • C ( 0 . 6 0 2 + 1 . 4 0 ) i j m/s2
  • D ( 0 . 6 0 4 + 1 . 2 4 ) i j m/s2
  • E ( 0 . 3 9 6 + 1 . 0 9 ) i j m/s2

Q4:

A particle is accelerated when acted on by two forces, as shown in the accompanying diagram. The force F has twice the magnitude of force F . Find the direction in which the particle’s net acceleration occurs, in terms of the angle below the negative 𝑥 -direction from the position of the particle.

Q5:

A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is the magnitude of its acceleration?

Q6:

Two forces of 25 and 45 N act on an object. Their directions differ by 7 0 . The resulting acceleration has magnitude of 10.0 m/s2. What is the mass of the body?

Q7:

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in the figure.

Find the magnitude of the total force on the Achilles tendon.

Q8:

A particle of mass 0.78 kg is acted on by the forces F i = 1 1 . 0 N , F i = 7 . 9 N , and F j = 8 . 1 N .

What is the particle’s acceleration?

  • A ( 2 . 0 + 4 . 5 ) i j m/s2
  • B ( 3 . 0 + 6 . 5 ) i j m/s2
  • C ( 6 . 0 + 1 5 ) i j m/s2
  • D ( 4 . 0 + 1 0 ) i j m/s2
  • E ( 5 . 0 + 1 2 ) i j m/s2

What displacement would result from 3.6 s of the acceleration produced by these forces?

  • A 8 8 j m
  • B ( 1 3 + 3 4 ) i j m
  • C ( 2 6 + 6 7 ) i j m
  • D 3 6 i m
  • E ( 5 2 + 1 3 4 ) i j m

Q9:

An object has a mass of 1.8 kg. The object changes from moving with velocity v i j k = ( 1 . 9 2 . 3 + 2 . 8 ) m/s at time 𝑡 = 4 . 5 s to moving with velocity v i j k = ( 1 . 1 + 0 + 1 . 7 ) m/s time 𝑡 = 7 . 0 s . What is the average force acting on the object?

  • A ( 2 . 2 + 1 . 7 0 . 7 9 ) i j k N
  • B ( 2 . 2 + 1 . 7 0 . 7 9 ) i j k N
  • C ( 2 . 2 1 . 7 0 . 7 9 ) i j k N
  • D ( 2 . 2 + 0 + 0 ) i j k N
  • E ( 2 . 2 1 . 7 0 . 7 9 ) i j k N

Q10:

A planet orbits a star, and the planet is orbited by a moon. At a particular time in the moon’s orbit around the planet, the gravitational force on the moon from the planet acts perpendicularly to the gravitational force on the moon from the star. The force on the moon from the planet, F = 1 . 2 1 × 1 0 N , and the force on the moon from the star, F = 5 . 0 0 × 1 0 N . The moon’s mass is 1 . 1 3 × 1 0 kg.

What is the magnitude of the moon’s resultant acceleration?

  • A 4 . 5 5 × 1 0 m/s2
  • B 8 . 5 5 × 1 0 m/s2
  • C 5 . 5 5 × 1 0 m/s2
  • D