Solutions Group Problem 7 - General Physics for Life Science | PHYS 2414, Study notes of Physics

Download Solutions Group Problem 7 - General Physics for Life Science | PHYS 2414 and more Study notes Physics in PDF only on Docsity! Physics 2414 Group Exercise 7 Name 1: OUID 1: Name 2: OUID 2: Name 3: OUID 3: Name 4: OUID 4: So lu tio ns So lu tio ns Section Number: Work and Energy A mass m moves from point ‘1’ to point ‘2’ under the action of the force ~F. Kinetic energy of the mass is given by the expression K = 1 2 mv2 (1) where v is the velocity of the particle. The change in kinetic energy of the mass is ∆K = Kf − Ki (2) = 1 2 mv2f − 1 2 mv2i (3) θ ~F ~d 1 2 Work done by the force ~F on the mass m is given by the expression W = |~F|d cos θ (4) where, ~d is the displacement of the mass m, and θ is the angle between the force vector and the displacement vector (see figure). The work done on the mass m equals the change in kinetic energy. The expression relating this is given by ∆K = W. (5) If there is more than one force acting on the mass, the change in kinetic energy equals the total work done by all the forces, and is 1 given by the expression ∆K = ∑ i Wi. (6) Problems A block of mass M = 100 kg slides on a frictional incline plane under gravity. The incline makes an angle θ = 30o with the horizontal. The coefficient of kinetic friction between the mass and the surface of the incline is µk = 0.25. The mass starts from the highest point on the incline plane and reaches the lowest point on the plane. The free body force diagram is provided to you. ~N~F f m~g θ ~N~F f y x m~g θ 1. Displacement vector: (a) If the base of the incline plane measures 5 meters, what is the magnitude of the displacement of the block. |~d| = 5 cos θ = 5 cos 30 = 5.75m (7) (b) Show the displacement vector ~d on the graph. y x ~d 2