Normal Force Example: Incline

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1 Normal Force Example: Incline α The angle of the frictionless incline is α = 30. Mass slides down the incline, starting from rest. What is the speed of the mass after it slid 10 meters downhill? [use g = 10 m/s 2 ] PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension

2 Newton s Third Law Lex Law III: Actioni To every contrariam action there semper is always et æqualem an equal esse and reactionem: opposite Law 3: In reaction: an sive interaction corporum the between forces duorum of two two actiones objects, bodies in on each se each mutuo other object are exerts semper always a esse force equal æquales on and the are other. et in directed partes These in contrarias two opposite forces dirigi. directions. are equal in magnitude and opposite in direction. m 2 PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension

3 Example: Two Blocks m 2 In the picture above, the two blocks are placed on a frictionless surface, in contact with each other. The masses of the two blocks are = 10 kg and m 2 = 15 kg. A force F 1 = 100 N is being applied to mass from the left, and force F 2 = 200 N is being applied to mass m 2 from the right. Compute the force F 2,1 that mass is exerting on mass m 2. PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension

4 Gravitational force Newton s Law of Gravitation: where m1 and m2 are the masses of the two bodies r is the distance between them, measured from the center of the (spherical) object G is the universal gravitational constant G = N m 2 / kg 2 provides excellent description of planetary motion PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension 4

5 Example: Cranial Attraction The heads of neighboring students in the classroom are separated by ~ 1 m. A typical human head weighs about 5 kg. Compute the attractive force (due to gravitation) between the heads of two students. F = G m 2 r 2 m1 = m2 = 5 kg, r = 1 m, G = N m 2 /kg 2 use in formula obtain F = N PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension 5

6 Example: Weight change while airplane is in flight An airplane is cruising at the altitude of 10 km above sea level. What factor less does a passenger weigh at that altitude compared to their weight at sea level? The radius of the Earth is 6370 km and its mass is ME = kg. F = G m 2 r 2 m1 = ME, m2 = m (unknown) Compare F(r) for r = RE to F(r) for r = (RE + 10 km) PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension 6

7 Example: g on surface of Mars F = G m 2 r 2 Declare this g when computed at the surface of a specific planet. Formula then simplifies to F = m 2 g For all objects on the surface of a planet, one of the masses (mass of the planet) and r are the same formula can then be simplified to F = m g, except g is different on each planet (depends on M and R) for Mars, MMars = 1/9 ME, RMars = RE we can then compute gmars in terms of gearth PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension 7

8 Tension Force Ideal String concept: massless, infinitely thin, fixed length withstands any force without breaking String with tension T m 2 PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension

9 Tension Example: Pulley + Weights The masses in the depicted Atwood machine are = 5 kg and m 2 = 3 kg. T 2 What is the acceleration of mass? What is the tension T 2 of the cable holding the massless pulley? m 2 PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, Tension

10 Friction Force due to imperfections of surfaces in contact For a pair of surfaces, the frictional force depends (only) on the normal force between the surfaces: Frictional force Normal force Coefficient of friction To a good approximation, does not depend on size or shape of contact surface, only the materials in contact Always opposite to the direction of motion Static friction objects not moving w.r.t. each other Kinetic friction one object is being dragged across PHY2053, Fall 2013, Lecture 7 Gravity, Contact Forces, the Tension (surface of the) other

11 Problem: Pushing a crate at an angle A crate of mass 100 kg is being pushed across a horizontal surface. The coefficient of friction between the crate and the surface is μ = 0.2. The force is being applied downward on the crate at a 30º angle with respect to the vertical axis. What is the minimum force at which the crate will move from its prone position? [use g = 10 m/s 2 ] F 30 PHY2053, Fall 2013, Lecture 6 Newton s Laws

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