Quiz #5 PHYCS 1500 22 February, 2006 Problem #1 (Serway & Faughn Chapter 5 Problem 76) A 2.00kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100N/m. The block is released from rest when the spring is unstretched, and the pulley is frictionless. The block moves 20.0cm down the incline before coming to rest. Find the coefficient of kinetic friction between the block and the incline. Answer: We can use the work-energy theorem to solve this problem. The only non-conservative force that does work on the block during its slide is friction, and both gravity and the spring contribute to the block’s potential energy. Wnc = ∆KE + ∆P E −Ff d = (KEf − KEi ) + (P Eg f − P Eg i ) + (P Esf − P Esi ) 1 −µFN d = (0 − 0) + (−mgd sin θ − 0) + ( kd2 − 0) 2 1 µmg cos θ = mg sin θ − kd 2 mg sin θ − 12 kd µ= mg cos θ (2.00kg)(9.80m/s2 ) sin 37◦ − 12 (100N/m)(0.200m) = (2.00kg)(9.80m/s2 ) cos 37◦ = 0.115 (1) (2) (3) (4) (5) (6) (7) Problem #2 (Serway & Faughn Chapter 5 Problem 78) An object of mass m is suspended from the top of a cart by a string of length L. The cart and object are initially moving to the right at constant speed v0 . The cart comes to rest after colliding and sticking to a bumper, and the suspended object swings through an angle θ (coming to rest there momentarily before swinging back down). a Show that the initial speed is p v0 = 2gL(1 − cos θ). 1 (8) Answer: No work is done on the object during its swing. 0 = ∆KE + ∆P E 1 = (0 − mv02 ) + (mg(L − L cos θ) − 0) 2 p p ⇒ v0 = 2g(L − L cos θ) = 2gL(1 − cos θ) b If L = 1.20m and θ = 35◦ , find the initial speed of the cart. Answer: p v0 = 2(9.80m/s2 )(1.20m)(1 − cos 35◦ ) = 2.06m/s 2 (9) (10) (11) (12)