Solutions for Physics Practice Test for Forces and Newton’s Laws
 

1. State any two of Newton's Laws in your own words and explain them using examples.

N1:  If an object is experiencing an acceleration (or change in velocity, or change in speed and/or direction) it must have a net force on it.  Likewise, if it does not have a net force on it, it will not accelerate.

Example: Consider the moon orbiting in a circle around the earth at constant speed.  Though its speed is not changing its direction is, so it is accelerating, hence it must have a net force on it.

N2:  An object of mass m will experience an acceleration a when a net force F_net is applied to it, such that:

F_net= ma  (the net force points in the same direction as the acceleration).

Example: If I (of mass 75 kg) were in outer space, away from any planet or star, and was being pulled by a rope with tension 100N to the right and a rope of tension 250N to the left I would feele a net force to the left of 150N.  From N2 I can calculate my acceleration algebraically as:

a = F_net/m

in this case it will give:

a = 150N left / 75 kg = 2.0 m/s² left

N3: If object 1 feels a force from object 2 (the action) then object 2 will experience the same size force from object 1 but in the opposite direction (the reaction).

Example: If I am standing on the ground and the ground pushes up on me with a normal force of 735N then I will push down on the ground with a normal force of 735N.

2. Consider a block of mass equal to your mass lying on a horizontal surface (μ_k=0.500 and μ_s=0.800 between the block and the surface). 
1. A rope is used to pull on the block with a force of magnitude 100N directed to the right.  Draw the free body diagram for the block showing all the forces and labeling them according to their type (normal, tension, weight, static friction, etc.) and value.

The diagram will show an arrow pointing down labeled “weight” and its value should be your mass times 9.8m/s².  Another arrow labeled “normal” will point up and have a value equal to your weight.  An arrow to the right will be labeled “tension” with a value of 100N.  An arrow to the left will be labeled “static friction” and have a value also of 100N, because 100N of tension is not sufficient to overcome the maximum static friction force =  μ_sN = 0.800*your weight which is undoubtedly greater than 100N.

2. Describe the reaction force for each of the forces.  (Think Newton’s Third Law.)

The normal force up from the surface on the block has a reaction force of the same magnitude from the block down on the surface.

The weight of the block down to the earth has a reaction force of the same size from the block pulling up on the earth.

The tension force of 100N right has a reaction force of 100N left of the block pulling on the rope.

The static friction force of 100N on the block to the right has a reaction force of 100N to the left of the block acting on the surface.

3. What is the maximum force that can be applied by the rope without the block moving?

the maximum static friction force =  μ_sN = 0.800*your weight

4. What will happen if the rope applies a force twice the magnitude of what you found in answer b)? (Be explicit. 

The block will move with an acceleration=a where Newton’s Second Law (N2) must be satisfied.  The net force will be a result of the force of twice that in c) above to the right = 1.6*your weight and the KINETIC friction force to the left of magnitude  =  μ_kN = 0.5*your weight, for a net force of 1.1*your weight to the right.  Using N2:

1.1*your weight = your mass*a, where your weight = your mass*g, so

1.1*your mass*g = your mass*a, so

1.1*g = a

The acceleration of the block will be 1.1*9.8m/s²= 10.78m/s² = 10.8m/s² if you do the sig figs.

5. How far will the block in question c) have traveled if it starts from rest and is pulled with that force for 3.0 s?

From the unit on motion x=½at²==½10.8m/s²(3.0s)²= 48.6m

3. Two blocks are hung over a frictionless, massless pulley, with a massless rope so that each mass hangs on one side of the pulley and the tension is constant throughout the rope.  The block on the right has a mass equal to the day of your birth (if you were born August 21^st, use a mass of 21 kg).  The block on the left has a mass of 40kg.
1. Draw a free body diagram for each block, assuming that the heavier block causes the pair of them to accelerate in its direction with an acceleration = a.

The block on the left will move down, the one on the right will move up, assuming you were born before the 40^th of the month! 

So, the diagram on the left will have an arrow up labeled T for the as yet unknown “tension” and one down labeled “weight” equal to 392 N.  There will be a floating arrow pointing down labeled a for the as yet unknown acceleration.

So, the diagram on the right will have an arrow up labeled T for the as yet unknown “tension” (same tension as for the other block) and one down labeled “weight” equal to your birth day*g.  There will be a floating arrow pointing up labeled a for the same acceleration as above.

2. Write the pair of equations you get by applying Newton’s Second Law (N2) to each diagram.

Assume up is positive for both diagrams (this looks ugly because everyone has a different “yourbirthday” for the mass in kg)

For the left block:

T - 392N = -40kg*a (note the minus sign on the right side of the equation, because the a is down, so negative)

For the right block:

T – yourbirthday*g = yourbirthday*a 

Solve the equations to get:

i.                     The tension in the rope.

T = 432N*yourbirthday/(40kg + yourbirthday)

ii.                   The acceleration of the blocks.

a = (392N – yourbirthday*g)/(40kg + yourbirthday)

 

4. A block of your mass is sliding down a ramp inclined 45˚ to the horizontal.
1. Draw the free body diagram for the block, choose and show a coordinate frame and draw an arrow representing the acceleration down the ramp labeled a.

The block will have an arrow pointing down labeled “weight” equal to yourmass*g.  Another arrow labeled “normal” points out perpendicular to the ramp and has value N, the yet to be found normal force.  The block will accelerate down along the surface of (parallel to) the ramp with acceleration a, the yet to be found acceleration.  The best coordinates are: x-axis parallel to the ramp, positive x in same direction as a; y-axis out from the ramp, parallel to normal force.

2. Write out the equations in the x and in the y directions from the diagram and using N2.

You need to take coordinates of the weight in the chosen system.  You get a component along positive x of yourmass*g*sin45º and along the negative y-axis of yourmass*g*cos45º.  Using N2:

y-axis (no acceleration):  N- yourmass*g*cos45º = 0

x-axis (acceleration = +a): yourmass*g*sin45º = yourmass*a

3. Solve the equations to find:

i.         The normal force on the block.

The first equation solves to give: N= yourmass*g*cos45º

ii.       The acceleration of the block.

The second equation solves to give a= g*sin45º= 7.0m/s²

 

4. Bonus: If μ_k=0.8 and μ_s=1.2 between the block and the ramp

i.         What will happen if the block is initially at rest?

I.        Find the friction force and the acceleration, if there is any.

The block will not slide since the static friction force is sufficient to keep it from moving. 

The force will be = yourmass*g*sin45º

ii.       What will happen if the block is initially in motion?

I.        Find the friction force and the acceleration, if there is any.

It will continue to slide.  The kinetic friction force will be =  μ_k N= μ_k*yourmass*g*cos45º, so the net force will be:

yourmass*g*sin45º - μ_k*yourmass*g*cos45º,  which by N2 is equal to yourmass*a, so:

 

a= g*sin45º - μ_k*g*cos45º = 1.4m/s²