# Solutions to Net Force

By Ben Winegar

Return to tutorial -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

-1. What is the weight of a 3.4 kg mass?
F = ma   Weight = force  F = 3.4 x 9.8 = 33.32 N

0. What mass has a weight of 720 N?
F = ma  720 = m x 9.8     m = 720/9.8   m = 73.5kg

1. Bob must exert 240 N of force on a 980 Kg car to move it at a constant speed up an incline. (The frictional force is 240 N) What is the acceleration of the car if he exerts a force of 350 N?
F = 350 - 240 = 110 N    F = ma    110 = 980 x a   a = 110/980    a = .112 m/s/s

2. What is the acceleration of a 6 Kg object hanging on a string that is under a tension of 80 N? 30 N? (Make up positive)
F = 80 - (9.8 x 6) = 21.2 N    F = ma     21.2 = 6 x a   a = 21.2/6    a = 3.5 m/s/s

F = 30 - (9.8 x 6) = -28.8 N    F = ma     -28.8 = 6 x a    a = -28.8/6    a = -4.8 m/s/s

3. What force is needed to accelerate a 60 Kg cart and rider from rest to 4.2 m/s in 2.5 seconds when the friction force is 24 N?
aav = Dv/Dt     aav  = 4.2/2.5 = 1.68     F = ma   (F - 24) = 60 x 1.68     F = 124.8 N

4. What is the mass of a box that moves at a constant velocity along a surface with a force of 15 N, and accelerates at 4.2 m/s/s when you exert 26 N?            F = ma     (26 - 15) = m x 4.2    m = 11/4.2     m = 2.6 kg

5. If you exert a force of 60 N on a car, it moves at a constant velocity. (i.e. there is a frictional force of 60 N) What is its mass if when you exert 80 N on it, it accelerates from rest to 2 m/s in 100 seconds?

aav = Dv/Dt       aav = 2/100 = .02    F = ma       (80 - 60) = m x .02   m = 20/.02   m = 1000 kg

6. A 60 Kg rocket accelerates upward from rest reaching a height of 23.4 m in 3.0 seconds. What must be the thrust of the engine?
s = ut + 1/2at2       23.4 = (0 x 3) + .5 a 3.0     23.4 = 4.5a   a = 5.2

F = 60 x 9.8 = 588    (F - 588) = 60 x 5.2       F - 588 = 312     F = 900 N

7. It takes 45 N to make a 10 kg cart move at a constant speed. What force does it take to make the cart accelerate at 3.2 m/s/s in the direction it is moving?
F = ma      (F - 45) = 10 x 3.2        F - 45 = 32      F = 77 N

8. What tension would accelerate a 5.0 Kg object suspended on a string upwards at 6.2 m/s/s? Downwards?
F = 5.0 x 9.8 = 49    F = ma      (F - 49) = 5.0 x 6.2     F - 49 = 31    F = 80 N

F = ma     (F - 49) = 5.0 x -6.2    F - 49 = -31      F = 18 N

9. A 45 gram rocket accelerates upward from 0 to 12 m/s in .05 seconds What must be the thrust of the engines?
aav = Dv/Dt       aav = 12/.05 = 240         F = .045 x 9.8 = .441     F = ma    (F - .441) = .045 x 240       F = 11.241 N

10. (Hard - Extra credit - won't be on the quiz!) A rocket has engines that produce 60 N of thrust. What is its mass if it accelerates upward at 40 m/s/s?
F = ma        (60 - 9.8m) = m x 40        60 = 49.8m       m = 1.2 kg