# 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.

**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/s
^{2} - B m/s
^{2} - C m/s
^{2} - D m/s
^{2} - E m/s
^{2}

**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/s
^{2} - B m/s
^{2} - C m/s
^{2} - D m/s
^{2} - E m/s
^{2}

**Q14: **

A rocket sled accelerates at a rate of 177 m/s^{2}.
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?

**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?

**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/s^{2}.

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?

**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/s^{2}.

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/s^{2}.

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