Physics Newton's First Law

1. A light hangs from two cables. One cable has a tension of 39.72 lb and is at an angle of 43.4o with respect to the ceiling. What is the weight of the lamp if the other cable makes an angle of 17.1o with respect to the ceiling?

a. 37.2 lb c. 36.8lb b. 35.8 lb d. 36.17lb

ans:36.17lb

2. A 46.07 N light hangs from two cables at angles 54.9o and 61.4o with respect to the ceiling. What is the tension in the first cable?

a. 24.6N c. 23.9N b. 25N d. 26.4N

ans: 24.6N

3. A light hangs from two cables. One cable has a tension of 28.75 N and is at an angle of 58.1o with respect to the ceiling. What is the tension in the other cable if it makes an angle of 9.4o with respect to the ceiling?

a. 15.9N c. 14.5Nb. 16.1N d. 14.9N

ans: 15.4N

Newton's Second Law

4. A 8.3 kg mass and a 17.1 kg mass are tied to a light string and hung over a frictionless pulley. What is their acceleration?

a. 33.95m/s2 c. 4.395 m/s2 b. 4 m/s2 d. 3.395 m/s2

ans: 3.395m/s2

5. An unknown mass and a 9.9 kg mass are tied to a light string and hung over a frictionless pulley. If the tension in the string is 14.5 N, what is the unknown mass?

a. 1kg c. 1.8kgb. 0.8kg d. 0.5kg

ans: 0.8kg

6.A lady pulls a cart with a force of 1837 N. Neglecting friction, if the cart changes from resting to a speed of 1.3 m/s in a distance of 0.03289 m, what is the total mass of the cart?

a.71.5kg c. 70.5kgb. 75.1kg d. 17.5kg

ans: 71.5kg

7.A 3.66 lb book is resting on a 19.41 lb table. What is the normal force from the floor on each table leg?

a. 5lbs c. 4.9lbsb. 5.7675lbs d. 6.7675lbs ans: 5.7675lbs

8. A box sits on a ramp inclined at 21.7o to horizontal. If the normal force on the box from the ramp is 20.94 N, what is the mass of the box?

formula: m * 9.8 * cos(21.7) = 20.94

a. 3.2 kg c. 2.3kgb. 2.9kg d. 3.9kg

ans:2.3 kg

9. A 7.9 kg box sits on a ramp. If the normal force on the box from the ramp is 41.82 N, what is the angle the ramp makes with the (horizontal) ground?formula: 7.9 * 9.8 * cos(theta) = 41.82

a. 75.3o c. 57.3ob. 57.5o d. 75.5o

ans: 57.3o

10. A man sees a 44.5 kg cart about to bump into a wall at 1.7 m/s. If the cart is 0.04203 m from the wall when he grabs it, how much force must he apply to stop it before it hits?

formula:

you can get the force required from Fnet=ma. You have 'm', so you need to find 'a'. get the acceleration from the kinematic part of the problem... a = (v2 - vi2)/2d (the final velocity = 0)

a. 1530N c. 1350Nb. 1250N d. 1520N

ans: 1530 N

11. What is the minimum force required to start a 4.2 kg box moving across the floor if the coefficient of static friction between the box and the floor is 0.6?

a. 23.761N c. 24.696Nb. 25.469N d. 26.496N

ans: 24.696N

12. What is the kinetic energy of a 70 kg man running along at 6.36 m/s? formula: KE = 1/2 * m*v2

a. 1315J c. 1215Jb. 1515J d. 1415Jans: 1415 J

13. What is the speed of a 53.6 kg woman running with a kinetic energy of 1617 J? sol'n: this is a straightforward application of the equation KE = 1/2 * m*v2 to solve for v, multiply both sides by 2, divide both sides by m, then take the square root of both sides

a. 7.77m/s c. 7.67m/sb. 7.57m/s d. 7.87m/s

ans: 7.77 m/s

14. What is the gravitational potential energy of a 149.1 kg man at a height of h = 74.21 m above the ground? (consider h=0 to be the reference where Ug=0) sol'n:

this is a straightforward application of Ug = m*g*h since m is in kg and h is in m, substitute in the values given with g = 9.8 m/s2 to get the energy in J

a. 100,000J c. 108,400Jb. 107,300J d. 110,580J

ans: 108,400 J

15. What is the height where a 121.2 kg woman would have a gravitational potential energy of 10610 J? (consider h=0 to be the reference where the Ug=0) sol'n:

this is a straightforward application of Ug = m*g*h substitute the m and Ug values given with g = 9.8 m/s2 then solve for h

a. 9.54m c. 8.94 mb. 7.57m/s d. 7.87m/s

ans: 8.94 m

16. What is the change in gravitational potential energy for a 68.9 kg man walking up stairs from a height of 63.07 m to 107.69 m? sol'n:

this is a straightforward application of {change in}Ug = m*g*{change in}h substitute the m and {change in}h (difference in heights) values given with g = 9.8 m/s2 then solve for

{change in}Ug

a. -30133 J c. 30320 Jb. 301230 J d. 30130 J

Answer: 30130 J

17. What is the change in gravitational potential energy for a 132.5 kg woman walking down a hill from a height of 102.86 m to 70.38 m? sol'n:

this is a straightforward application of {change in}Ug = m*g*{change in}h

substitute the m and {change in}h (difference in heights) values given with g = 9.8 m/s2 then solve for {change in}Ug

note that the change in height is negative

a. -4123 J c. -5 Jb. -42175 J d. 4321 J

Answer: -42175 J

18. How much work is done by gravity when a 82.3 kg diver jumps from a height of 5.23 m into the water? sol'n: the amount of work equals the change in gravitational potential energy this is m*g*(change_in_height)

a. 4321 J c. 4871 Jb. 4218 J d. 4334 J

Answer: 4218 J

19. How much work must be done to move a 34.6 kg box 3.66 m across the floor if the coefficient of kinetic friction between the box and the floor is 0.3.

sol'n: work=distance*Ffriction

a. 372.3 J c. -372.3 Jb. -321.9 J d. 3.234 J

ans: 372.3 J

20. What is the coefficient of kinetic friction between a 16 kg box and the floor if it takes 140.4 J of work to move it a distance of 3.2 m? sol'n:

draw a free body diagram write out the horizontal and vertical force equations rearrange work=distance*Ffriction=distance*coefficient*m*g to solve for the coefficient of kinetic friction

a. 0.28 c. 0.281 b. -0.25 d. 0.21

Answer: 0.28

21. What is the length of a 73.7 m wide rectancular slab if its mass is 1.01 kg and the moment of intertia about an axis through the center and perpendicular to the large flat face if its mass is 713.6 kg*m2?

a. 55.2m c. 52.5mb. 53.5m d. 54.5m

ans: 55.2m

22. What is the mass of a hollow cylinder of radius 3.38 m if it has a moment of inertia of 33.930468 kg*m2 about the central axis or rotation?

a. 3.07kg c. 2.97kgb. 2.50kg d. 1.95kg

ans:2.97kg

23. A 0.324 kg ball is stuck 0.54 m from the center of a disk spinning at 5.55 rad/s. What is its angular momentum? a. 0.5243J*s c. 1.021J*s

b. 0.6321J*s d. 1.1524J*s

ans: 0.5243J*s

24. A 40.2 kg child is sitting on the edge of a 165.3 kg merry-go-round of radius 2.1 m while it is spinning at a rate of 3.229 rpm. If the child moves to the center, how fast will it be spinning? (Hint: use conservation of angular momentum)

a. 4.5rpm, c. 4.2rpmb. 4.4rpm d. 4.8rpm

ans:4.8rpm

25. An empty metal can rolling down a hill gets to the bottom with a speed of 1.06 m/s. What would have been the speed if the can was full? (assume the ends of the hollow can don't significantly affect its moment of inertia and the walls are so thin that the full can may be considered as a solid cylinder of the same radius)

a. 1.333m/s c. 1.223m/sb. 1.423m/s d. 1.323m/s

ans:1.223m/s

26. A light hangs from two cables. One cable has a tension of 23.83 lb and is at an angle of 26.2o with respect to the ceiling. What is the weight of the lamp if the other cable makes an angle of 48.7o with respect to the ceiling?

a. 34.86 lb c. 35.8 lb b. 33.9lb d. 36lb

ans: 34.86 lb

27. A light hangs from two cables. One cable has a tension of 25.55 N and is at an angle of 7.5o with respect to the ceiling. What is the tension in the other cable if it makes an angle of 20.2o with respect to the ceiling?

a. 28 N c. 27 Nb. 26N d. 29 N

ans: 27N

28. A man is pulling a cart (total 26.7 kg) with a force of 1612 N. Neglecting friction, how much time does it take to get the cart from rest up to 1.5 m/s?

Soln: use the mass and force to find the acceleration, use the acceleration and the initial and final speeds to get the time (the initial speed is 0)

a. 0.04583s c. 0.03567sb. 0.01252s d. 0.02484 s

ans: 0.02484 s

29. A lady is pulling a cart (total 55.7 kg) with a force of 395 N. Neglecting friction, what is the acceleration of the cart?

a. 7.1 m/s2 C. 7.091 m/s2 b. 7.092 m/s2 d. 7.093 m/s2

ans: 7.091 m/s2

30. A lady pulls a cart with a force of 1454 N. Neglecting friction, if the cart changes from resting to a speed of 1.7 m/s in a distance of 0.02872 m, what is the total mass of the cart?

a. 28.90 kg c. 27.90 kg b. 28.91 kg d. 29.00 kg

ans: 28.90 kg

31. A man sees a 44.5 kg cart about to bump into a wall at 1.7 m/s. If the cart is 0.04203 m from the wall when he grabs it, how much force must he apply to stop it before it hits?

Soln: you can get the force required from Fnet=ma. You have 'm', so you need to find 'a'. get the acceleration from the kinematic part of the problem... a = (v2 - vi2)/2d (the final velocity = 0)

a. 1530 N c. 1630 N b. 1730 N d. 1830 N

ans: 1530 N

32. A 5.4 kg mass and a 6.2 kg mass are tied to a light string and hung over a frictionless pulley. What is the tension in the string?

Soln: start with a free-body diagram write out the force equations on each mass the tension in the string is the same at both ends the value of the acceleration is the same for both masses, but one accelerates up, the other accelerates

down eliminate the acceleration from the two equations to find the tension (if you found it easier to solve for acceleration, use it in one of the equations to find the tension)

a. 56.57 N c. 57.1 N b. 55.569 N d. 56.569 N ans: 56.569 N

33. A 4.6 kg mass and an 8.5 kg mass are tied to a light string and hung over a frictionless pulley. What is their acceleration? a. 2.92 m/s2 c. 2.917 m/s2 b. 2.916 m/s2 d. 3 m/s2

ans: 2.917 m/s2

34. An unknown mass and a 13.2 kg mass are tied to a light string and hung over a frictionless pulley. If the tension in the string is 61.3114 N, what is the unknown mass? a. 4.1 2kg c. 4.0 kg b. 4.1 kg d. 4.2kg

ans: 4.1 kg

35. A 3.1 lb book is resting on a 73.76 lb table. What is the normal force of the book on the table? a. -3.2lbs c. 3.2lbs b. -3.1bs d. 3.1 lbs ans: -3.1 lbs

36. A 5.2 kg box sits on a ramp inclined at 42.4o to horizontal. What is the normal force on the box from the ramp? a. 37.64N c. 37.54 N b. 37.53N d. 37.63 N

ans: 37.63 N

37. A 6.7 kg box sits on a ramp inclined at 37.4o to horizontal. What is the normal force on the ramp from the box?

a. 52.17N c. -52.16 N b. 52.16 N d. -52.17 N ans: -52.16 N

37. A box sits on a ramp inclined at 21.7o to horizontal. If the normal force on the box from the ramp is 20.94 N, what is the mass of the box? a. 2.3 kg c. 2.2kg b. 2.4kg d. 2.1kg ans: 2.3 kg

38. A 7.9 kg box sits on a ramp. If the normal force on the box from the ramp is 41.82 N, what is the angle the ramp makes with the (horizontal) ground? a. 57.3o c. 57.4 o b. 563o d. 55.3 0 ans: 57.3o

39. What is the minimum force required to start a 11.5 kg box moving across the floor if the coefficient of static friction between the box and the floor is 0.64? a. 72.13N c. 72.13 N b. 72.1 N d. 72.128 N

ans: 72.128 N

40. What is the mass of a box which requires a minimum pushing force of 74.088 N to start moving across a floor with a coefficient of static friction between the box and the floor of 0.6? a. 12.2kg c. 13kg b. 12.6 kg d. 12.5kg

ans: 12.6 kg

41. If a minimum force of 79.4682 N is required to push on a 15.9 kg box to begin moving it across the floor, what is the coefficient of static friction between the box and the floor?

a. 0.51 c. 0.53 b. 0.52 d. 0.54

ans: 0.51

42. A box is sliding down a ramp with an acceleration of 1.621 m/s2. If the ramp is at an angle of 25.1o relative to the ground, what is the coefficient of kinetic friction between the box and the ramp? a. 0.2857 c. 0.2856 b. 0.3000 d. 0.2867

ans: 0.2857

43. What is the kinetic energy of a 70 kg man running along at 6.36 m/s? Soln:

this is a straightforward application of the equation KE = 1/2 * m*v2 simply plug the numbers into the right hand side

a. 1416J c. 1415 J b. 1417J d. 1418J

ans: 1415 J

44. What is the change in gravitational potential energy for a 68.9 kg man walking up stairs from a height of 63.07 m to 107.69 m?

Soln: this is a straightforward application of {change in}Ug = m*g*{change in}h substitute the m and {change in}h (difference in heights) values given with g = 9.8 m/s2 then solve for

{change in}Ug a. 30130 J c. 30131 J b. 30132J d. 30133 J

ans: 30130 J

45. What is the mass of a diver whose gravitational potential energy changes by -160,500 J when diving into water from a height of 130.61 m? a. 125.2 kg c. 125.5 kg b. 125.3 kg d. 125.4 kg

ans: 125.4 kg

46. How much work is done by gravity when a 82.3 kg diver jumps from a height of 5.23 m into the water? a. 4220 J c. 4229 J b. 4218 J d. 4219 J

ans: 4218 J

47. What height above the water does a 133.9 kg diver jumps need to jump from for gravity to do 6062 J of work on him/her? a. 4.61 m c. 4.62 m b. 4.60 m d. 4.63 m ans: 4.62 m

48. What is the mass of a diver if gravity does 8100 J of work on him/her when jumping into the water from a height of 6.55 m? What is the mass of a diver if gravity does 8100 J of work on him/her when jumping into the water from a height of 6.55 m?]

a. 126.2 kg c. 126.4 kg b. 126.1 kg d. 126.3 kg ans: 126.2 kg

49. How much work must be done to move a 34.6 kg box 3.66 m across the floor if the coefficient of kinetic friction between the box and the floor is 0.3? a. 372.2 J c. 372.4 J b. 372.3 J d. 372.5 J

ans: 372.3 J

50. What is the coefficient of kinetic friction between a 16 kg box and the floor if it takes 140.4 J of work to move it a distance of 3.2 m? a. 0.28 c. 0.27 b. 0.29 d. 0.3 ans: 0.28

51, What is the mass of a box which requires 3518 J of work to be pulled 9.36 m across a floor with a coefficient of kinetic friction between the box and the floor of 0.4? a. 96 kg c. 95.7 kg b. 95.8 kg d. 95.9 kg

ans: 95.9 kg

52.How far must you pull a 10.9 kg box across the floor to do 123.3 J of work if the coefficient of kinetic friction between the box and the floor is 0.15? a. 7.5 m c. 7.7 m b. 7.6 m d. 7.8 m ans: 7.7 m

53. How much work must be done to move a 3.8 kg chair 6.1 m across the floor at constant velocity if the coefficient of kinetic friction between the chair and the floor is 0.64 and you are pushing at an angle of 30.2o relative to the floor? a. 231.5 J c. 231.7 J b. 231.6 J d. 231.8 J

ans: 231.6 J

54. If you do 231.9 J of work to move a 19.8 kg chair 3.35 m across the floor at constant velocity, and you are pushing at an angle of 17.9o relative to the floor, what is the coefficient of kinetic friction between the floor and the chair? Soln:

draw a free body diagram write out the horizontal and vertical force equations... use force*sin(theta) & force*cos(theta) so there is only

one force unknown you have three unknowns in these two equations - force applied, normal force, coefficient of kinetic friction use work=forcehorizontal*distance to obtain a third equation you now have three equations & three unknowns - it is now just an algebra problem my suggestion... use the work equation to find the horizontal force then use the angle to find the magnitude of the force

your vertical force equation should now tell the value of the normal force now use forcehorizontal = forcefiction = coefficient*{normal force} solve this last equation for the normal force

a. 0.30 c. 0.32 b. 0.31 d. 0.33

ans: 0.32

55. A 80.4 kg diver jumps from a height of 2.64 m with an initial speed of 1.25 m/s. What is his speed entering the water? Soln:

the diver's mass was given to make it easier to use energy formulas, however, it will cancel in the mass and is hence irrelevant

the change in gravitational potential energy (mgh - where 'h' is the change in height hf-hi) equals (negative of) the change in kinetic energy

solve for the final kinetic energy from the final kinetic energy and the mass calculate the final speed

a. 7.301 m/s c. 7.303 m/sb. 7.302 m/s d. 7.304 m/s

ans: 7.301 m/s