Newton's 2nd Law - Practice Problems and Solutions

This video covers Newton's 2nd law by covering many practice problems with full solutions. We begin every problem with a picture and free-body diagram, then apply Newton's 2nd Law. This is done by summing the forces along each direction, setting this net force equal to the mass of the object times the acceleration in that direction, and finally solving for what we are interested in. After following these steps for each object, including applying Newton's laws for each direction, we will have everything we need to find our solution. Problems involving interacting objects that require more care with respect to Newton's 3rd law will be covered in another video. 0:15 - A gymnast is suspended by a rope connected to the ceiling by an O-ring. If the weight of the gymnast is 500 N, find the tension in the tope and the force on the ceiling from the O-ring. 3:06 - A crate is suspended by a rope connected to an O-ring. The O-ring is held in place by a rope connected to a wall and another connected at a 60 degree angle to the ceiling. Assuming you know the weight, find the tension in each rope in terms of the weight. 6:56 - A car sits on a ramp that makes an angle of 30 degrees with the horizontal ground. If the car weighs 1.80 x 10^4 N and is held in place by a cable, (a) find the tension in the cable, and (b) find the normal force on the car. 9:15 - An Atwood machine in made of two objects that are connected by a string over a pulley. We take the pulley and string to be massless. Here we have an Atwood machine consisting of a crate on a ramp and a suspended bucket. If the objects are to move at a constant speed, find the weight of the bucket in terms of the weight of the cart. 11:11 - A key is hanging by a string from the rear-view mirror of a car. When the car accelerates, the key is deflected by an angle phi. This angle will depend on the acceleration. If we call the mass of the key m, find the acceleration in terms of the mass and angle. 13:03 - A crate is sliding down a frictionless ramp where the slope of the ramp makes an angle theta with the horizontal. Find the magnitude of acceleration a, and normal force n. 14:04 - An Atwood machine consists of a box sitting on a flat surface and a bucket suspended by a pulley. The object move together maintaining tension in the rope that connects them. Find the acceleration of each object and the tension in the rope. 15:47 - In order to get a 500 N crate to start moving, a 230 N force must be applied. To keep the crate moving, a 200 N force is needed. Find the coefficients of friction mu_s and mu_k. 17:46 - If you pull at an angle of 30 above horizontal, how hard must you pull to keep a crate weighing 500 N moving at a constant velocity? Also, find the normal force. Take the coefficient of kinetic friction to be 0.40. 19:20 - A sled slides down a ramp that slopes at just the right angle to slide with constant velocity. Find the angle in terms of the weight and coefficient mu_k. 21:27 - A vertical spring stretches 1.00 cm when a 12.0 N wieght is attached at its end. When the weight is replaced with a 1.50 kg block, what diestance will the spring stretch? 23:37 - Your weight of 1000 N is supported by 200 identical springs of a mattress which compresses 2.6 cm when yo lay on them. Find the spring constant k of the springs. 24:38 - A car weighing 15,000 N is being towed up a 25 degree slope at constant velocity. Friction can be neglected. If the tow rope is rated for a maximum tension of 5000 N, find if the rope will break. 25:31 - Carol pushes a 25 kg wooden box across a wooden floor at a steady speed of 2.0 m/s. How much force does Carol exert on the box? If she stops pushing, how far will the box slide? Take the coefficient of kinetic friction to be 0.20. 28:05 - A 50 kg metal box sits on the bed of a dump truck making an angle of 20 degrees to the horizontal. What is the size of the static friction force f_s on the box? At what angle would the box slide if mu_s is 0.80 and mu_k is 0.60? 29:47 - A 2.0 kg book is pushed against a wall at an angle that is 25 degrees above the horizontal. If mu_k = 0.20, find the magnitude of the force needed for the book to slide down at a constant speed.