Worksheet: Systems of Unbalanced Forces

In this worksheet, we will practice applying Newton's second law of motion and Newton's third law of motion to analyze systems of forces that produce a net force that is not zero.


A hot-air balloon has a mass of 350 kg. The balloon is near the ground, and two ropes were thrown out for people on the ground to grab onto in order to help pull the balloon to the ground. Before the ropes are pulled, the balloon accelerates vertically downward at 0.25 m/s2. And when the ropes are pulled, it accelerates downward at 1.5 m/s2. Each rope has the same force applied to it, and each person pulling on the rope has a mass of 75 kg. How many newtons does each person who holds a rope apparently weigh while holding onto it?


A cyclist supplies a force of 250 N to her bicycle. She and the bicycle together have a mass of 130 kg. The bicycle accelerates at 1.5 m/s2 as it travels into a headwind that applies a 15 N force in the opposite direction to the bicycle’s velocity, and friction acts on the bicycle in the same direction as the wind. How much force, in newtons, is supplied by friction?


A car with a mass of 320 kg is having engine problems, so it is being towed behind a van while the driver of the malfunctioning car tries to start its engine. The van supplies a force of 960 N to the car, and a friction force of 160 N acts in the opposite direction to the car’s motion. The malfunctioning motor starts to work and provides the car with a force of 160 N. What is the acceleration of the car when its engine starts working?


A piano of mass 300 kg is moved along a horizontal surface by a person pushing from one side and another person pulling from the other. The piano accelerates at 0.25 m/s2. The pushing force is 120 N, and a friction force of 60 N acts in the opposite direction to the piano’s velocity. What is the pulling force? Consider the direction in which the piano moves to be the positive direction.


An object has three forces acting on it, as shown in the diagram. What is the magnitude of the net force on the object?


Three demolition workers push on a wall. The workers push with forces of 80 N, 50 N, and 60 N on the same side of the wall, parallel to each other. What is the total force acting on the wall?


An airplane with a mass of 3,000 kg flies horizontally at a constant speed. The airplane then increases its horizontal speed and the lift force produced by its wings increases to 30 kN, increasing the airplane’s altitude. How much has the airplane’s altitude increased by when it has an instantaneous upward velocity of 25 m/s?


A boy and a girl play tug-of-war with a rope, as shown in the diagram. The boy accelerates the girl toward him by pulling the rope through his hands, and while he does this a friction force of 15 N acts on the girl in the opposite direction to her movement due to the friction of her shoes with the plastic-coated floor.

What force does the boy apply on the rope?

If instead the boy has smooth slippers on his feet that produce no friction force, when he pulls the rope, at what rate does he accelerate toward the girl?


A man with a mass of 85 kg sits down on a chair with a mass of 35 kg that uses a spring to adjust its height. The chair and the man accelerate together downward at 1.2 m/s2. The base of the chair exerts a net force of 164 N downward while the chair accelerates downward. How much upward force does the spring in the chair exert during the downward acceleration of the chair seat?


A slice of an extremely cheesy pizza is lifted from a plate by a 4.5 N upward force, stretching the melted cheese. Strands from the remaining pizza stick the slice to the plate, as shown in the diagram. The cheese strands pull the rest of the pizza and the plate the pizza rests on upward. The slice and plate accelerate upward at 3.5 m/s2. The mass of the pizza and plate is 250 g. What is the force required to stretch the strands of cheese?


A car has a velocity of 25 m/s as it passes a road sign. At that point, the car’s wheels push the car forward with a force of 550 N, and the friction between the car’s wheels and the road applies a force of 550 N in the opposite direction to the car’s motion. What is the velocity of the car 10 seconds after it passes the sign? Assume no other forces act in this time.

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