AP Physics B Summer Course 2012 2012年AP物理B暑假班 Ch 12: Newton’s Second Law, Fnet = ma M Sittig AP Physics B Summer Course 2012 2012年AP物理B暑假班

Four-Step Problem Solving for Newton’s 2nd (force) Problems 1. Draw a proper free-body diagram. 2. Resolve vectors into their components. 3. For each axis, set up an expression for Fnet, and set it equal to ma. 4. Solve your system of equations.

Key points to remember A net force causes an acceleration, and an acceleration means there is a net force. Net force and acceleration must be in the same direction. Only Fnet is equal to ma, setting single forces = ma is playing with fire.

Types of problems Blocks on planes Blocks on inclines Pulleys/strings Atwood machines Elevator rides

Blocks on planes

Example Problem

Practice Problem Two blocks are in contact on a frictionless table. A horizontal force F is applied to M2. If M1 = 2 kg, M2 = 4 kg and F = 6 N, find the size of the contact force between the two blocks.

Practice Problem Two blocks are in contact on a frictionless table. A horizontal force F is applied to M1. If M1 = 2 kg, M2 = 4 kg and F = 6 N, find the size of the contact force between the two blocks.

Practice Problem Two blocks of equal masses are placed on a horizontal table as shown. The bottom block is then pulled with a slowly increasing horizontal force F. The coefficients of static friction for both surfaces are greater than zero and equal to each other. Select the correct description of the motion of the blocks. (continued…)

Practice Problem The top block begins to move as soon as F reaches a certain minimum value; the bottom block does not move at that instant but would begin to move as F increases further. The top block begins to move as soon as F reaches a certain minimum value; the bottom block would never move even as F increases further. Both blocks begin to move simultaneously as reaches a certain minimum value; as F increases further, both blocks always have the same acceleration. The bottom block begins to move as soon as F reaches a certain minimum value; the top block does not move at that instant but would begin to move as F increases further. Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the bottom block exceeds the acceleration of the top block. The bottom block begins to move as soon as F reaches a certain minimum value; the top block would never move even as F increases further. Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the top block exceeds the acceleration of the bottom block. The 5th.

Practice Problem Two blocks of equal masses are placed on a horizontal table as shown. The top block is then pulled with a slowly increasing horizontal force . The coefficients of static friction for both contact surfaces are greater than zero and equal to each other Select the correct description of the motion of the blocks. (continued…)

Practice Problem Two blocks of equal masses are placed on a horizontal table as shown. The top block is then pulled with a slowly increasing horizontal force . The coefficients of static friction for both contact surfaces are greater than zero and equal to each other Select the correct description of the motion of the blocks. (continued…)

Practice Problem The top block begins to move as soon as F reaches a certain minimum value; the bottom block would never move even as F increases further. Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the top block exceeds the acceleration of the bottom block. The top block begins to move as soon as F reaches a certain minimum value; the bottom block does not begin to move at that instant but would begin to move as F increases further. Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, the acceleration of the bottom block exceeds the acceleration of the top block. Both blocks begin to move simultaneously as F reaches a certain minimum value; as F increases further, both blocks always have the same acceleration.

Blocks on inclines

Example Problem

Practice Problem If an automobile’s braking distance from 100 km/hr is 60 m on level pavement, determine the automobile’s braking distance when it is going up a 6° incline. Hint: What force causes the braking auto to decelerate?

Pulleys/strings

Example Problem A frictionless pulley with zero mass is attached to the ceiling, in a gravity field of 9.81 m/s2. Mass m1 = 0.15 kg is accelerating downward at 1.1 m/s2. Find M2.

Practice Problem A 1.97 kg mass is suspended from a string which is pulled upward. The mass accelerates upwards with an acceleration of 2.30 m/s2. What is the tension in the string?

Atwood machines

Example Problem M1 and M2 are connected by a string over a massless, frictionless pulley. Describe the motion of M2 when: A) the table is frictionless. B) the coefficient of kinetic friction between the table and M1 is mu.

Practice Problem Block m1 goes up on an inclined plane (θ = 15o) with acceleration a = 3.49 m/s2. It is connected with m2 = 4 kg by a string that passes over a frictionless pulley. Knowing that the pulley is massless and the coefficient of friction on the inclined plane is μk = 0.5, find m1.

Super Challenge Problem

More Challenge Problem Two prisms are placed as shown. Angle θ (see the diagram) is given. The coefficient of static friction between the touching surfaces of the prisms is μ. The bottom prism is pushed along a horizontal surface. What is the range of accelerations of the bottom prism that allows the top prism to remain at rest relative to the bottom one?

Elevator rides

Example Problem Daniel weights himself in an elevator that accelerates downward with constant acceleration a = 2 m/s2. If Daniel's mass is m = 65 kg, find what the scale from the elevator will show.

Elevator Demo Let’s take a ride in the elevator! On a scale!

Practice Problem Starting from rest, an elevator accelerates uniformly between the 1st and 2nd floors, and decelerates uniformly between the 5th and 6th floors, coming to a stop at the 6th floor. Between the 2nd and 5th floors, the elevator covers the 6 meter distance between two adjacent floors in 1 second. Inside, Liz (who is about to graduate) is standing on a scale that reads 800 N when the elevator isn’t moving. What was her minimum scale reading during the trip? Use g = 10 m/s2.

Practice Problem A student is riding an elevator in the Acme Building, and the elevator is moving a constant upward speed. Which plot shows the tension T in the elevator cable as a function of time?

Practice Problem A student steps onto a bathroom scale in a stationary elevator on the first floor of the Acme Building. The elevator accelerates until it reaches the second floor and then continues at constant speed until the 5th floor, where it starts slowing and stops on the 6th floor. Which sketch of the apparent weight (reading of the scale) vs. time during the entire process is most likely to be correct?

Newton’s 3rd Law Forces come in pairs. If Fm,E, then FE,m. Why don’t N3 pairs cancel out? Example: I kick a ball, there is a force of foot-on-ball and a force of ball-on-foot, why does the ball move?