AP Physics 1 Notes Forces
Types of Forces: Forces are often referred to as the “pushes” and “pulls” in nature, and there is quite a variety of them. We will discuss the following forces extensively during this unit.
Gravity: The attractive force between any two bodies within the universe.
FG = G m1 m2
R2
G is the universal gravitational constant and is equal to 6.67 x 10-11.
m1 and m2 are the masses of the two objects.
R is the distance between the centers of masses of the two objects.
Normal: The force applied by a surface when an object is pressed against it. This force acts perpendicular to the surface.
Tension: This is the force that a string or rope exerts on a body.
Friction: This type of force always resists the natural motion of an object.
f = μFN
f is the frictional force
μ is the coefficient of friction and it describes the nature of the interaction between the two surfaces rubbing against each other.
Spring: The force exerted by a spring varies as the string is stretched.
Fs = k x
k is the spring constant for the spring and is measured in N/m x is the distance the spring is elongated or compressed
Free-Body Diagram: Free-body diagrams are used to indicate the directions of forces acting on a body.
Examples:
1. Bottle resting on a table:
2. Mass on a string:
Weight: The net force of gravity on an object.
Fw = mg
m = mass of the object (kg)
g = acceleration due to gravity (9.8m/s2)
Weight, like other forces is measured in N (newtons). Therefore, 1N = 1 kg m/s2. Vector Nature of Forces:
A 10 kg box rests on an incline of 25° as seen, below.
1. On the diagram below, draw and label vectors indicating all forces acting on the box.
2. As a class, draw the parallel and perpendicular components of the weight on the top diagram.
3. Determine the value of the weight component that is parallel to the surface of the plane.
4. Since the box is at rest, what will be the value of the frictional force?
5. Determine the value of the normal force acting on the box.
6. How would the vector diagram change if we reduced friction by using a cart instead of a box? How does that change the status of the object?
1 st Law of Motion : An object having a particular velocity will continue with that
velocity until a net force acts upon it. (Inertia)
2 nd Law of Motion : Σ F
x = m ax
Σ means sum. We some refer to this as the “sum” of the forces or the “net” force.
The subscript “x” indicates that the net force and acceleration are in the same direction.
1. What is the acceleration of the cart below?
1 N 3 N
2. What is the tension in the string below?
Accelerating upward at 1.5 m/s2
3 rd Law of Motion : For every action force there is an equal and opposite reaction force.
F1 = -F2
1. Someone hits a door with a force of 5 N. According to Newton’s third law, what happens simultaneously?
2. How does Newton’s third law apply to a bug hitting a windshield? 4 kg
Apparent Weight: The apparent weight is the weight that an object seems to weigh as it is accelerating.
A 50 kg person stands on a scale in an elevator as it moves. Determine the scale readings under the following conditions:
a. Accelerating upwards at 2 m/s2.
b. Accelerating downward at 4 m/s2.
c. Moving at a constant speed of 10 m/s upward.
Gravitational Forces
1. What is the gravitational force between my hand and the Celtic Rock?
2. What is the gravitational force between the moon and the earth? Mass of Earth = 5.9736 x 1024 kg
Mass of Moon = 7.349 x 1022 kg
Avg. Distance = 3.8 x 108 m
4. What is the acceleration due to gravity on the surface of Mars? Mass of Mars = 6.4 x 1023 kg
Radius of Mars = 3.4 x 106 m
5. A block has a weight of W on Earth. What will be its weight on a planet with a mass 6 times the mass of earth and a radius 3 times that of earth? Answer in terms of W.
Friction
Coefficient of Friction:
µs = coefficient of static friction (not sliding: Generally greater than µk)
µk = coefficient of kinetic friction (sliding)
Discuss the interaction between surfaces:
Formula involving Coefficient of Friction:
f = µ Fn
Demo:
1. Use a spring scale to determine the force required to slide a box at a constant velocity along the plane.
3. According to Newton’s 1st Law of Motion, an object with a constant velocity has
a net force equal to _______. Therefore: a. Fs = _______
b. FN = _______
4. Determine the mass of the box using a scale.
5. Calculate the kinetic coefficient of friction between these surfaces.
Problems:
1. A horizontal force of 60 N is just enough to get a box started sliding to the right on a horizontal table. The box has a weight of 30 N.
a. Draw a free-body diagram for this situation.
b. What is the force of friction applied on the box?
c. What is the normal force on the box?
d. What is the coefficient of friction between the two surfaces?
2. A 1.5 kg box moves at a constant speed to the right across a tabletop while a 12 N force is applied to it to the right.
b. What is the box’s acceleration?
c. What is the frictional force on the box?
d. What is the normal force on the box?
e. What is the coefficient of kinetic friction between the surfaces?
3. If the box in problem 2 now has a force of 16 N applied to it, instead of the 12 N force, on the same tabletop, what will be its acceleration?
4. A 10 kg box is pulled along a flat horizontal surface with a constant force of 3 N. When the box reaches a speed of 10 m/s, it encounters a constant frictional force of 8 N.
a. Draw a free body diagram of this event.
c. How much time will it take for the box to come to a stop?
d. How far will the box travel before coming to rest?
2-Body Motion:
1. Discussion: How catapult roller coasters shoot you out of the station so fast?
2. Set up as diagramed. Put a 1 kg mass in the cart, and a 100 gram mass as the hanging mass.
1 kg mass
1
2 100 g mass
a. Draw a free-body diagram of the forces acting on the 1 kg cart. Use Newton’s 2nd law to develop an expression involving the forces acting on
the 1 kg cart.
1
b. Draw a free-body diagram of the forces acting on the 100 g mass. Use Newton’s 2nd law to develop an expression involving the forces acting on
2
c. Combine the equations in parts a and b to develop an equation for the acceleration of the cart as the mass falls.
d. Predict the acceleration of the cart. i. while the mass is falling
ii. while the mass is on the ground and the cart is on the plane
iii. while the mass is on the ground and the cart has left the plane.
f. How far horizontally does the cart travel from the plane to the floor?
Continuation: Set-up the apparatus with the 50 gram mass 60 cm from the floor.
1 kg mass
50 g mass
1. Use a stopwatch to measure the time that it takes to cause the 50 g mass to fall 60 cm.
2. Calculate the acceleration of the 1 kg cart based on the time above.
3. Determine the frictional force between the cart and the surface.
