Newton s Laws II Physics Objectives i) Distinguish weight and mass, and understand that weight is a force ii) What is Normal force and when does this force exist? iii) Practice solving questions ΣF=ma when force is applied at an angle using trigonometry functions iv) Recognize the advantage of the using an inclined plane and practice solving problems using ΣF=ma Weight is a Force The force of gravity is the force with which the Earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the Earth. Our body also has mass and the force of gravity due to Earth is pulling on our body against the surface, which results in weight force. The man s mass is being pulled down against the surface of the Earth due to the gravitational force, resulting in weight. Our weight only exists if there is surface that stops up from falling. Expression of weight in mathematical form; The unit of weight => ( ) Force of gravity(f g) Weight = ( ) ( ) Since weight is a force, and force is always expressed as ΣF=ma, weight is also expressed as F g = ( ) *~some textbook use W g for weight where g is acceleration due to gravity, which is always g = -9.8m/s 2 Important: When we create a weight vector using gravity, we will use its magnitude (9.8 m/s 2 ) with an angle of 270. 1
Q1) If we were placed on the moon, does our mass change? What about our weight? Normal Force Q2) How many forces are acting on the block at rest below? a) One! b) Two! c) Four! d) Infinite forces! *Various Cases of Motion F=ma I. Applied Force(F app) at an Angle Q3) A crate with a mass of 23kg accelerates along a frictionless surface as the crate is pulled with a force of 14.5N at an angle of =19, as shown below. What is the horizontal acceleration of the crate? ( See solution next page for reference) a) 1.4m/s 2 b) 0.427m/s 2 c) 1.29m/s 2 d) 0.58m/s 2 2
Solution for Q3) step1) Draw an arrow to represent the force vector step2) Draw x-y coordinate. step3) Divide the force into components using trigonometry step4) Using Newton's 2nd law to solve ; F=ma sin19 Y Fg =mg FN 19 x cos19 X : F x= cos19 =ma x Y : F x= FN +sin19 mg=ma y Since the problem asks us to find only the horizontal acceleration, we will not consider any motion in the in the y-direction(if any). So we only need to use the equation in the x-direction. Since F app=14.5n, solving for 'a' gives a x= 14.5cos19 =0.58m/s 23 2 F=ma Q4) Two forces act on a 4.5kg block resting on a frictionless surface as shown below. What is the horizontal acceleration of the block? F 1 =5.9N at an angle of 43, F 2=3.7N. a) 1.8 m/s 2 b) 1.2 m/s 2 c) 0.82 m/s 2 d) 0.13 m/s 2 F1 F2 Q5) Two forces act on a 4.5kg block resting on a frictionless surface as shown below. What is the horizontal acceleration of the block? F 1 =5.9N at an angle of 43, F 2=3.7N. a) 1.8 m/s 2 b) 1.2 m/s 2 c) 0.82 m/s 2 d) 0.13 m/s 2 F1 F2 3
F=ma II. Motion on an Inclined Plane - An inclined plane is one of the commonlyrecognized simple machines. - Advantage The inclined plane permits one to overcome a large resistance by applying a relatively small force through a longer distance (compared to raising the load vertically) easier! harder! - Examples of inclined planes Ramps, slopes Q6) How much force is needed to give a 5kg block an acceleration of 2m/s² up the 30º incline plane? Assume the inclined plane is frictionless. Solution is on next page! a) 45.6N b) 39.5N c) 34.5N d) 29.5N 4
Solution for Q6) i) Draw a free-body diagram to identify the forces acting on the block ii) Draw x-y coordinate. The x-axis must be parallel to the direction of motion y FN x Fg iii) If any force is not aligned x or y axis, divide that force into components iv) Write the equations using ΣF x=ma x and ΣF y=ma y y Fgsin FN x ΣF x= F app - F gsin = ma x, ΣF y= F N - F gcos = 0 (since a y =0) v) Solve for F app F app = mgsin + ma x ( F g = mg) = 5 9.8 sin30 + 5 2 = 34.5N Fg Fgcos Q7) Find the force needed to give a 5kg block an acceleration of 2m/s² up the incline plane when the angle is 10 and 5. Assume the inclined plane is frictionless. i) when =10 ii) when =5 5
F=ma Q8) An 8kg box is released on a 30º inclined plane and slides down a frictionless inclined plane. i) Find the acceleration of the box. ii) Does the mass affect the motion of the box? (*~the box is sliding due to gravity, so there is no applied force) a) 4.9m/s 2 b) 3.4m/s 2 c) 2.2m/s 2 d) 1.4m/s 2 iii) From above, find the acceleration of the box when the angle is =20, =10 and =5. Q9) A block is pushed up a frictionless 30 incline by an applied force as shown. If F app=25n and m=3.0kg, what is the magnitude of the resulting acceleration of the block? a) 2.3m/s 2 b) 4.6m/s 2 c) 3.5m/s 2 d) 2.9m/s 2 e) 5.1m/s 30 30 6