Physics 300 – Tension Problems
Mr. Youker
1. A 500 g ball is suspended from the ceiling by a single vertical cord.
Determine the tension within the cord.
a = Fnet/m
0 = (FT – Fg)/m
FT = mg
FT = (0.5)(9.8)
FT = 4.9 N
2. A crane lifts a 2000 kg broken down car vertically upward at a rate of 40 cm/s by means
of a single vertical cable. Determine the tension within the crane’s cable.
a = Fnet/m
a = (FT – FG)/m
a = (FT – mg)/m
0 = (FT – (2000)(9.8))/2000
0 = (FT – 19,600)/2000
0 = FT – 19,600
FT = 19,600 N
3. A 80 kg mountain climber descends a cliff, accelerating downward at a rate of 0.20 m/s2.
Determine the tension in the climber’s rope.
a = Fnet/m
a = (FG – FT)/m
a = (mg - FT)/m
0.20 = ((80)(9.8) - FT)/80
0.20 = (784 - FT)/80
16 = 784 - FT
FT = 768 N
4. A 300 kg piano is accelerated upwardly off of the ground by means of two vertical ropes,
each carrying 1700 N of tension. At what rate is the piano accelerating?
a = Fnet/m
a = (FT + FT – FG)/m
a = (FT + FT – mg)/m
a = (1700 + 1700 – (300)(9.8))/300
a = (1700 + 1700 – 2940)/300
a = 460/300
a = 1.5 m/s2
5. Find the mass of a potato if it produces 22 N of tension in the spring from which it is
suspended.
a = Fnet/m
a = (FT – FG)/m
a = (FT – mg)/m
0 = (22 – (m)(9.8))/m
0 = 22 – (m)(9.8)
9.8 m = 22
m = 2.2 kg
6. A toy airplane flies around and around in a horizontal circle, tethered to a central axis by
a 3 m long string. The plane completes 5 revolutions in 4 seconds of time. The tension in
the string is 200 N. Find the speed of the plane, the centripetal acceleration of the plane,
the mass of the plane.
v = d/t
v = 5(2r)/t
v = (5)(23)/4
v = 94.2/4
v = 23.6 m/s
ac = v2/r
ac = 23.62/4
ac = 139 m/s2
a = Fnet/m
ac = FT/m
139 = 200/m
m = 1.4 kg
7. A 20 g ball is attached to the end of a 80 cm long string. The breaking tension of the
string is 200 N. Find the maximum speed that the ball may be whirled around in a circle.
a = Fnet/m
ac = FT/m
v2/r = FT/m
v2/0.80 = 200/0.020
v = 89 m/s
8. Tarzan jumps down from a branch that is high above a river. He swings down on a vine
that is 5 m long… obtaining a maximum speed of 12 m/s as he passes above the river. If
Tarzan has a mass of 120 kg, then determine the tension in the vine at the lowest point in
his swing.
a = Fnet/m
ac = (FT – Fg)/m
v2/r = (FT – mg)/m
122/5 = (FT – (120)(9.8))/120
28.8 = (FT – 1176)/120
3456 = FT – 1176
FT = 4632 N
9. How much tension is required to lift a 2 kg mass vertically upward at a constant speed?
a = Fnet/m
0 = (FT – Fg)/m
FT = mg
FT = (2)(9.8)
FT = 19.6 N
10. What final speed will result when a 30 kg box is pulled 3 m horizontally over a
frictionless surface (from rest) by a rope with 5 N of tension in it?
vf2 = vi2 + 2ad
vf2 = 02 + 2(a)3
vf2 = 6(0.167)
vf2 = 1
vf = 1 m/s

a = Fnet/m
a = FT/m
a = 5/30
a = 0.167 m/s2