APC -Unit 2

2 nd Law A 72kg person stands on a scale which sits on a floor of elevator. It starts to move from rest upward with speed v(t) = 3t + 0.2t 2, b) If elevator is at x =10m when t =2.0s, find location at t = 4.0s a) f ind scale reading at t = 4.0s.

Equilibrium When net force in all directions is zero 60 o 30 o 15N A B Find the tension in cable A and B

A circus performer of weight W is walking along a "high wire" as shown. The wire bends and makes a shallow angle below the horizontal. The tension in the wire is: a) depends on whether he stands on one or two feet b) much more than W c) much less than W d) approximately W/2 e) approximately W

System Acceleration A block of mass M and a block of mass m are connected by a thin string that passes over a light frictionless pulley. Find the acceleration of the system using only variables and constants.

Three blocks are connected as shown. Find the tension in the rope connecting the block on table. Assume no friction & massless rope. Find system acceleration using only variables and constants. Now find tension

Find tension in rope on left assuming smooth table surface

example An object of mass 5.0 kg is subjected to a rightward force in newtons of F = 3t 2 – 4t where t is measured in seconds. The object has velocity v = 7.0m/s, left at t = 2.0s. Determine the velocity & acceleration of the object at t = 9.0s.

Inclined Plane θ θ θ Φ

A 7.5kg shopping cart is accelerated up the incline at a rate of 1.4m/s 2. Incline is angled at 13 o and no friction is present. A)Determine the value of the force, F, in the horizontal direction (0 o ) needed to do this. B)Determine value of normal force on cart F

The diagram shows four choices for the direction of a force of magnitude F to be applied to a block on an inclined plane. The directions are either horizontal or vertical. (For choices a and b, the force is not enough to lift the block off the plane.) Rank the choices according to the magnitude of the normal force on the block from the plane, greatest first.

Friction (f) A force that acts parallel to surfaces in contact with one another. Two types are kinetic and static. fsfs F APP

Static friction > Kinetic friction Example 20 o A 10 kg box is pulled with a force of 30N along a rough floor (μ k = 0.30) as shown. a)Draw FBD of ALL forces acting on box b)Determine the acceleration of the box.

Determine the acceleration of the masses assuming coefficient of kinetic friction is 0.2.

Determine the tension in rope assuming massless.

In random pairs, determine and submit on paper your answer with justification.

More Calculus Needed! *u substitution Natural Log properties:

U-Substitution There are times when the power rule is not an option for use as an integration technique. Example: For times greater than 0, an object beginning at the origin moves in one dimension according to the following expression: Find the distance traveled by the object during the first 10 seconds.

An equation that relates a quantity and its derivatives is called a differential equation. In APC Physics, we only need to be familiar with a few basic Diff E q’s. The independent variable will always be time, t. The acceleration of an object is given by the following function: Derive an expression for the velocity as a function of time assuming initial conditions are that x = 0 and v = 4m/s at t=0. Differential Equations

EXAMPLE: The acceleration of a particle, a = –1.2x–0.8x 3 and when x = +5m, v = 4m/s. Determine how far does the particle travel before coming to rest? (note ‘a’ is given in terms of x)

Integrating e at 2 EXAMPLES

A particle moves in one dimension with a velocity as follows: v(t) = 5e -t/2 Find the displacement of the particle from t = 0 to t = 4s.

An object falls from rest from a large distance. Due to gravity and air drag, the velocity of object follows the equation: v(t) = 60 (1-e -t/10 ) Find an expression for the displacement as a function of time.

Force proportional to v Consider a mass (m) that experiences a resistive force of air, F = -bv, where b is positive constant. Find v as function of t. F drag mg Take down to be positive

Air resistance handout

If a force F(t) = F o e -kt acts on mass, m, that is initially at rest, what is the expression for the final velocity of object as time approaches infinity?

Bosun Chair Is there a difference in the tension in the rope attached to the chair in the 2 situations? If so, what? The tension is half in the picture on the left of what it is on the right since chair is supported by 2 ropes instead of 1

Assume massless, frictionless pulley & massless rope. With what force must the man pull on the rope to rise at constant speed? Force on rope

Circular Motion (F NET =ma for circles) Centripetal Force, F C, is a special way to say F NET

If an object is experiencing uniform circular motion, is it in equilibrium? Consider amusement park ride of the rotating swings. Swingcars rise into air until they reach a steady height. Find the speed of each swingcar if chain length is 5.0m and the angle btw vertical and chain is 35 o

The RotoRide involves spinning people in ac circle like the spin cycle of a washing machine. Once the ride gets upto speed, the floor drops and you don’t slide. Find minimum period for this to occur assuming the radius of the ride is R and coefficient of static friction is u S.

Force analysis of car without friction What force provides F C on car to be able to perform circular motion? What speed does car need to execute curve without friction assuming radius of curve is R and angle of curve is θ? Banked Curve

If friction needs to act (recall friction doesn’t always need to be present), which direction will it point?