Lesson: Systems of Unbalanced Forces

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?