# 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 m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

Q2:

An object with a mass of 5.0 kg accelerates at a rate of 2.0 m/s2 in the positive -direction when two forces are applied to it. One of the forces acts in the positive -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 m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

Q4:

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

What is the particle’s acceleration?

• A m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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

• A m
• B m
• C m
• D m
• E m

Q9:

An object has a mass of 1.8 kg. The object changes from moving with velocity at time to moving with velocity at time . What is the average force acting on the object?

• A N
• B N
• C N
• D N
• E 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 , and the force on the moon from the star . The moon’s mass is kg.

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

• A m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

Q11:

Two children push a wagon horizontally and in opposite directions. The first child pushes the wagon forward with a force of 56.2 N, while the second child pushes with a force of 82.6 N and produce a friction force of 10.3 N. The mass of the wagon is 38.5 kg. Assume that forward displacement of the wagon corresponds to positive values.

What is the resultant acceleration of the wagon?

What is the resultant acceleration of the wagon if the friction force is 18.6 N?

Q12:

A sailboat that has a mass of kg is at sea. The wind is exerting a force on the boat’s sails of N in the direction of north of east. There is an ocean current pushing on the sailboat toward the east with a force of N.

What is the magnitude of the acceleration produced by the resultant force on the sailboat?

At what angle north of east is the sailboat accelerated?

Q13:

A soccer game is viewed from a helicopter above the playing field. During this game, two soccer players simultaneously kick a stationary soccer ball on the flat field. The soccer ball has mass 0.420 kg. One player kicks the ball with force 162 N at an angle north of west. At the same instant, the other player kicks the ball with force 215 N at an angle east of south. Find the net acceleration of the ball.

• A m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

Q14:

A rocket sled accelerates at a rate of 177 m/s2. The sled’s passenger has a mass of 82.3 kg.

Calculate the horizontal component of the force the seat exerts against the passenger’s body.

• A N
• B N
• C N
• D N
• E N

What is the ratio of the passenger’s weight to the force exerted on them by the sled’s acceleration.

Calculate the magnitude of the total force that the sled’s seat exerts against the passenger’s body.

• A N
• B N
• C N
• D N
• E N

Calculate the angle above the horizontal at which the total force that the sled’s seat exerts against the passenger’s body acts.

Q15:

Two ropes are attached to a tree, and forces of and are applied. The forces are coplanar.

What is the resultant of these two force vectors?

• A N
• B N
• C N
• D N
• E N

What is the magnitude of the resultant of these two force vectors?

At what clockwise angle from the positive -axis does the resultant of these two force vectors act?

Q16:

An object has a mass of 2.3 kg. The object accelerates at 3.2 m/s2 in the positive -direction, under the influence of the forces and . acts in the positive -direction with a magnitude of 9.7 N. What is the magnitude of ?

Q17:

As a flea jumps it exerts a force of N vertically downward on the ground. The flea pushes vertically upward against an air current that exerts a force of N vertically downward on the flea. The flea has a mass of kg. What is the magnitude of the flea’s net upward acceleration when it jumps?

Q18:

A fireman has a mass of 83.2 kg. He hears the fire alarm and slides down a fire pole with an acceleration of 5.33 m/s2. What is the magnitude of the force that the fireman exerts on the pole as he slides down it?

Q19:

A diving board is 8.25 m above the water in a swimming pool. A swimmer jumps off the board into the water and comes to rest 2.56 s after entering the water. The swimmer has a mass of 73.3 kg. Assuming that air resistance during the dive was negligible, what average upward force did the water exert on the swimmer?

Q20:

A particle has a mass of 2.3 kg. The acceleration of the mass is m/s2. Two forces are acting on the mass. One of the forces is N. What is the magnitude of the other force?

Q21:

A rugby player is being pushed backward by an opposing player. The opposing player is pushing with 679 N of force. The player being pushed backward has a mass of 83.2 kg, and is accelerating backward at 1.04 m/s2.

What is the magnitude of the friction force from the ground against the backward motion of the rugby player?

The opposing player has a mass of 101 kg. What force does this player apply to the ground to move forward?

Q22:

A rocket sled has a mass of kg. The sled’s rockets provide an accelerating force of N. The surface on which the sled moves produces a friction force on the sled N. What is the magnitude of the acceleration of the sled?

Q23:

A figure skater has a mass of 40 kg and her partner’s mass is 50 kg. She pushes against the ice with a force of 120 N, causing her and her partner to move forward. Calculate the pair’s acceleration. Assume that all forces opposing the motion, such as friction and air resistance, total 5.0 N.

Q24:

A car of mass 1,100 kg pulls a boat on a trailer. The mass of the boat and the trailer together is 700 kg. The car exerts a force of 1,900 N on the road and produces an acceleration of 0.550 m/s2.

What total force resists the motion of the car, boat, and trailer?

What is the force in the hitch between the car and the trailer if of the resisting forces are experienced by the boat and the trailer?

• A N
• B N
• C N
• D N
• E N

Q25:

A tractor with a mass of 2,200 kg pushes an airplane out of a passenger loading area, exerting a force of N backward on the pavement. The system experiences forces resisting motion that total 2,800 N. The acceleration of the airplane is 0.175 m/s2.

What is the mass of the airplane in kilograms?

• A kg
• B kg
• C kg
• D kg
• E kg

Calculate the force exerted by the tractor on the airplane, assuming 2,400 N of the friction is experienced by the airplane.

• A N
• B N
• C N
• D N
• E N