PHYS 1401 College Physics I HOMEWORK PROBLEMS CRN 55178 Khalid Bukhari HW 4 Chapter 4 THE LAWS OF MOTION PART A Hand in your answers in class on scantron on Wednesday 22 September 2010 The questions have been numbered so you can use the back side of an older scantron Write your name class 1401 and HW 4 on the scantron 1 A horizontal force of 95 0 N is applied to a 60 0 kg crate on a rough level surface If the crate accelerates at 1 20 m s2 what is the magnitude of the force of kinetic friction acting on the crate a 23 0 N b 45 0 N c 16 0 N d 33 0 N e 8 80 N Newton s second law gives the net force acting on the crate as Fnet 95 0 N fk 60 0 kg 1 20 m s 2 72 0 N This gives the kinetic friction force as fk 23 0 N so choice a is correct 2 A 70 0 kg man stands on a pedestal of mass 27 0 kg which rests on a level surface What is the normal force exerted by the ground on the pedestal a 265 N b 368 N c 478 N d 624 N e 951 N Since the pedestal is in equilibrium the normal force pressing upward on its base supports the total weight of the man and pedestal Therefore or n Fg man Fg pedestal mman m pedestal g 97 0 kg 9 80 m s2 951 N showing that e is the correct choice 3 Two monkeys of equal mass are holding onto a single vine of negligible mass that hangs vertically from a tree with one monkey a few meters higher than the other What is the ratio of the tension in the vine above the upper monkey to the tension in the vine between the two monkeys a b 1 c 1 5 d 2 e More information is required The tension Fupper in the vine at the point above the upper monkey must support the weight of monkey both monkeys i e Fupper 2 Fg single However the tension in the vine between the two monkey monkeys supports only the weight of the lower monkey Flower Fg single meaning that Fupper Flower 2 and choice d is correct 4 A force of 70 0 N is exerted at an angle of 30 0 below the horizontal on a block of mass 8 00 kg that is resting on a table What is the magnitude of the normal force acting on the block a 43 4 N b 78 4 N c 113 N d 126 N e 92 4 N Because the block has zero vertical acceleration Newton s second law says that SFy F sin 30 0 mg n 0 or 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 4 n 70 0 N sin 30 0 8 00 kg 9 80 m s2 35 0 N 78 4 N 113 N and we see that c is correct 5 If Earth s mass and radius both suddenly doubled what would the new value of the acceleration of gravity near Earth s surface a 9 80 m s2 b 4 90 m s2 c 2 45 m s2 d 19 6 m s2 e 12 6 m s2 From Newton s law of universal gravitation the force Earth exerts on an object on its surface is Fg GM E m RE2 mg or the acceleration of gravity at Earth s surface is g GM E RE2 If both the mass and radius of the Earth should double so M E 2 M E and RE 2 RE the acceleration of gravity at the surface would then be g G M E 2 M 1 M g 9 80 m s2 G 2E G 2E 4 90 m s2 4 R 2 R 2 2 E E RE 2 meaning that b is the correct answer 6 A crate remains stationary after it has been placed on a ramp inclined at an angle with the horizontal Which of the following statements must be true about the magnitude of the frictional force that acts on the crate a It is larger than the weight of the crate b It is at least equal to the weight of the crate c It is equal to sn d It is greater than the component of the gravitational force acting down the ramp e It is equal to the component of the gravitational force acting down the ramp When the crate is held in equilibrium on the incline as shown in the sketch Newton s second law requires that SFx SFy 0 From ur SFx F g r fs 0 the magnitude of the friction force equals the component of gravitational force acting down the incline or choice e is r r correct Note that fs s max ms n only when the crate is on the verge of starting to slide x 8 A manager of a restaurant pushes horizontally with a force of magnitude 150 N on a box of melons The box moves across the floor with a constant acceleration in the same direction as the applied force Which statement is most accurate concerning the magnitude of the force of kinetic friction acting on the box a It is greater than 150 N b It is less than 150 N c It is equal to 150 N d The kinetic friction force is steadily decreasing e The kinetic friction force must be zero 9 Four forces act on an object given by 40 N east 50 N north 70 N west and 90 N south What is the magnitude of the net force on the object a 50 N b 70 N c 131 N d 170 N e 250 N Choose a coordinate system with the positive x direction being east and the positive y direction being north Then the components of the four given forces are Ax 40 N Ay 0 C x 70 N C y 0 Bx 0 By 50 N Dx 0 Dy 90 N The components of the resultant or net force are Rx Ax Bx C x Dx 30 N and Ry Ay By Cy Dy 40 N Therefore the magnitude of the net force acting on the object is 2 PHYS 1401 College Physics I R Rx2 Ry2 CRN 55178 30 N 2 40 N 2 Khalid Bukhari HW 4 50 N or choice a is correct 10 If an object of mass m moves with constant velocity v the net force on the object is a mg b mv c ma d 0 e None of these answers is correct 11 If an object is in equilibrium which of the following statements is not true a The speed of the object remains constant b The acceleration of the object is zero c The net force acting on the object is zero d The object must be at rest e The velocity is constant 13 A large crate of mass m is placed …