Motion with Constant Acceleration PHYSICS 220 Lecture 03 Motion with Constant Acceleration Textbook Sections 3.1 Lecture 3 Purdue University, Physics 220

Graphing calculator are not allowed during exams. Because they it can store nearly everything in memory. Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Exercise Where is velocity zero? Where is velocity positive? Where is velocity negative? Where is speed largest? position vs. time Where is acceleration zero? Where is acceleration positive? If speed is increasing, v and a are in same direction. If speed is decreasing, v and a are in opposite direction. velocity vs. time Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Question A skydiver is falling straight down, along the negative y direction. During the initial part of the fall, her speed increases from 16 to 28 m/s in 1.5 s. Which of the following is correct? A) v>0, a>0 B) v>0, a<0 C) v<0, a>0 D) v<0, a<0  correct v a During a later part of the fall, after the parachute has opened, her speed decreases from 48 to 26 m/s in 11 s. Which of the following is correct? A) v>0, a>0 B) v>0, a<0 C) v<0, a>0 D) v<0, a<0  correct v a Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 iClicker A ball is tossed from the ground up a height of two meters above the ground and falls back down. Draw v vs t v -2 t 4 3 A B C D E Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Tossed Ball y A ball is tossed from the ground up a height of two meters above the ground and falls back down. t v Draw v vs t Draw y vs t Draw a vs t t a t Lecture 3 Purdue University, Physics 220

Apply Newton’s law to calculate how things will move Spacecraft with engine on a=F/m (Newton’s second law) v = v0 + at (equation for straight line) How to find position versus time relation? x = x0 + v0t + 1/2 at2 Can we relate velocity only to position change? v2 = v02 + 2a(x-x0) (Demonstrate at home) Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Question A car accelerates uniformly from rest. If it travels a distance D in time t then how far will it travel in a time 2t? A) D/4 B) D/2 C) D D) 2D E) 4D Correct x=1/2 at2 Follow up question: If the car has speed v at time t then what is the speed at time 2t? A) v/4 B) v/2 C) v D) 2v E) 4v Answer 1: E Answer 2: D Correct v=at Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Kinematics Example A car is traveling 30 m/s and applies its breaks to stop after a distance of 150 m. How fast is the car going after it has traveled ½ the distance (75 meters) ? A) v < 15 m/s B) v = 15 m/s C) v > 15 m/s This tells us v2 proportional to Dx Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Newton’s Second Law SF = ma Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Example A force F acting on a mass m1 results in an acceleration a1. The same force acting on a different mass m2 results in an acceleration a2 = 2a1. What is the mass m2? (1) 2m1 (2) m1 (3) 1/2 m1 F a1 m1 a2 = 2a1 m2 F=ma F= m1a1 = m2a2 = m2(2a1) Therefore, m2 = m1/2 Or in words…twice the acceleration means half the mass Lecture 3 Purdue University, Physics 220

Problem Solving Recipe Identify the object(s) of interest. Draw the free-body diagram for each object, showing all the forces acting on it. Choose a coordinate system. Find the net force along each axis. Use Newton’s second law to find the acceleration along each axis. Find the velocity and displacement along each axis from the acceleration. Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Free Body Diagrams Isolate the object of interest Identify all forces acting on object and represent them as vectors Choose a coordinate system (e.g., x,y,z) Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Example A tractor T is pulling a trailer M with a constant acceleration. If the forward acceleration is 1.5 m/s2, calculate the force on the trailer (m=400 kg) due to the tractor (m=500 kg). Neglect friction. x–direction y x N T W Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Example A tractor T (m=500 kg) is pulling a trailer M (m=400 kg). It starts from rest and pulls with constant force such that after 10 seconds it has moved 30 meters to the right. Calculate the driving force on the tractor. y x X direction: Tractor SF = ma Fw – T = mtractora Fw = T + mtractora T Fw W N T W N Combine: Fw = mtrailera + mtractora Fw = (mtrailer + mtractor ) a X direction: Trailer SF = ma T = mtrailera Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Example A tractor T (m=500 kg) is pulling a trailer M (m=400 kg). It starts from rest and pulls with constant force such that after 10 seconds it has moved 30 meters to the right. Calculate the driving force on the tractor. y x Combine: Fw = mtrailera + mtractora Fw = (mtrailer + mtractor ) a T Fw W N T W N Acceleration: Dx = v0t +1/2 a t2 a = 2 Dx / t2 = 0.6 m/s2 FW=900kg0.6m/s2 FW = 540 Newtons Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 iClicker If an object is acted on by two finite constant forces, is it possible for the object to move at constant velocity? A) No, it will accelerate B) Yes, the forces must be perpendicular C) No, it will follow a curved path D) Yes, the forces must be equal and opposite E) Yes, the forces must be in the same direction Answer: D Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Frame of Reference Motion is relative. Motion can be described only after a frame of reference is chosen. A frame of reference may be in motion with respect to other frames of reference. The description of motion in one frame of reference may be mathematically transformed into that in another frame of reference. In a frame of reference, different coordinate systems may be used to describe motion. Lecture 3 Purdue University, Physics 220

Inertial Frame of Reference Any reference frame in which Newton’s laws are valid is called an inertial frame of reference If no net force acts on a body (FNET = 0) there is no acceleration acting on the body, i.e. it moves with constant velocity M F1 F2 F3 F4 Lecture 3 Purdue University, Physics 220