I. Warm-up Exercises

1. Newton’s laws form the foundation of classical mechanics. Carefully state these three important laws.

2. Each of the situations described below can be best explained in terms of one of Newton’s three laws.  State which of the three laws corresponds to each of the following situations, and clearly explain why you made the choice you did.

(a) It usually surprises people to find out that they are pulling on the earth with a force equal in magnitude to their weight!

(b) You are driving your friend’s pickup truck down a straight road with a box in the truck bed.  You suddenly make a sharp turn to the right.  When you do so, the box in the back slides  to the left-hand side of the truck.

(c) A rocket engine works by pushing fuel quickly out the back end of a nozzle in the engine, thus providing a forward thrust on the rocket.

(d) From the upward acceleration of the spider, we know that there must be a relatively large force in the thread of webbing pulling it up.

3. Your friend Barb is sitting on a sled.  You push the sled forward such that the net force acting on Barb and the sled is 120 N.  Barb is seen for a short time to accelerate at 1.6 m/s².  What is the mass of Barb if the sled has a mass of 13 kg?

4. The horizontal force of the wind on the sails of a sailboat is 350 N in the direction 78^o North of East.  The water exerts a horizontal force of 210 N in the direction due East.  The boat has a weight of 3,000 N.  (a) What is the magnitude and direction of the resultant force acting on the boat due to the wind and water forces given above?  (b) What is the corresponding equilibrant force?  (c) What is the acceleration of the boat assuming that no other forces affect the boat’s motion?

5. A particle of mass 0.78 kg experiences two forces. Force F₁ of magnitude 3.4 N acts at a 47^o angle measured counterclockwise from the positive x-direction. Force F₂ of magnitude 4.7 N acts at a 12^o angle measured clockwise from the negative y-direction. (a) What is the resultant force acting on the particle? (b) What is the equilibrant force? (c) What is the acceleration of the particle?

6. You kick a block of mass 3.7 kg so that it slides to the right across the floor. A friction force of magnitude 11 N points towards the left.  (You don’t have to understand anything about friction here — just the magnitude and direction of the force!) (a) What is the value of the normal force exerted on the block by the floor?  (Make sure that you draw a FBD and apply Newton’s 2nd law to solve this problem!)  (b) What is the acceleration of the block?

7. You are pushing a 75-kg friend across a very slippery frozen pond.  You push horizontally towards the right with a force of 90 N.  (a) What is your friend’s resulting  acceleration? (b) How long does it take for your friend to reach a speed of 3.0 m/s assuming that he was a rest when you started pushing him?

II. Some Standards

8. A truck is towing a 1,200-kg car on a horizontal road with a chain.  The chain makes a 15^o angle above the horizontal as it pulls on the car.  (Neglect any frictional effects in this problem.) The car is being accelerated at 0.57 m/s² by the chain. (a) What is the tension in the chain?  (Hint: Draw a good FBD and apply Newton’s 2nd law to the x-direction. There should be three forces shown on your FBD!) (b) What is the car’s apparent weight as it is being towed with the acceleration given above?

9. A large 5.6-kg box is sliding down a frictionless inclined plane of angle q.  The box has an acceleration of 4.3 m/s².  (a) What is the value of the angle of incline, q?  (Hint:  You’ll need the inverse-sine function for this.  Do you remember how the inverse-tangent function worked?  See your instructor if you don’t understand this function.) (b) What is the box’s apparent weight as it slides down the incline?

10. Crazy Isaac has come up with another crazy idea, but much to Monica’s surprise, this one might actually work.  Isaac has been upset about the fact that a car has a speedometer to determine its  speed, but not an accelerometer to measure its acceleration.  The accelerometer that he designed is actually quite simple: it consists of a protractor, a string, and a weight.  The weight is tied to the end of the string, and then the other end of the string is attached to the inside top of the car. Isaac claims that he can determine the acceleration of the car simply by measuring the angle q that the string makes with the vertical at any instant of time. Help out Isaac (and convince Monica) by determining the acceleration of the car when q = 17^o.

III. So, you think you’re pretty good...?

11. Turner Fernswopper (known by only his closest friends as Twinkie) makes a career of being different from everyone else, and the recent weather has given him no excuse to do otherwise.  While the other kids are jumping on their sleds and then speeding down the hill, Twinkie places his sled at the bottom of the hill and facing up the hill. He then runs, jumps on the sled, and sees how far he can slide up the slope before stopping.  On a particularly good run, Twinkie finds that he slides up the hill (which looks amazingly like an inclined plane!) a distance of 2.5 m.  Since the hill is covered with snow and ice, it is for all practical purposes frictionless.  The mass of Twinkie and his sled is 65 kg , and the angle of inclination of the hill is 22^o.

(a) Draw a FBD showing Twinkie as he is sliding up the hill on his sled. Just to see how things work out, let the positive x-direction point up the hill.

(b) Determine Twinkie’s x-component of acceleration as he is sliding up the hill.

(c) What was Twinkie’s initial speed at the base of the hill (that is, at the instant that he was at the bottom of the hill and starting to slide up)?

12. A small block of mass m is shot up a frictionless incline of angle q with an initial speed v_o .  The block moves up the incline a distance D before stopping and starting to slide back down the incline. Find an expression for the distance D in terms of constants and the quantities m, v_o, and q.

13. A 2.0 kg block and a 5.0 kg block are attached by means of a string which runs over a pulley, as shown in the figure below.  The 2.0-kg block slides on a frictionless incline of angle 37^o.  The blocks are released  from rest.  What are the values of the acceleration magnitude and the tension in the string after the blocks are released?