# 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.

**Q1: **

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/s^{2}. And when the ropes are pulled, it accelerates
downward at 1.5 m/s^{2}. 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?

**Q2: **

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/s^{2}
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?

**Q3: **

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?

**Q4: **

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/s^{2}. 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.

**Q7: **

An airplane with a mass of 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?