What is the Speed and Maximum Height of a Pendulum Bob in Motion?

[kissafilipino]

A 1.0 N pendulum bob is set into motion on a 75 cm long string. At the bottom of the swing the tension is 1.2 N.

a) Deduce that the speed of the bb at the bottom of the swing is 1.2 m s^-2
b) Determine the maximum height the bob will swing assuming no air resistance or friction.

Homework Equations

a) v = 2(pie)r/T = n2(pie)r/t
F = ma
F = m(v^2/r)

The Attempt at a Solution

I first tried setting up a FBD to make it clear, and then after for question B, I simply used F = ma to find the mass, then after finding the mass, the speed:

F = ma
1.2 = m(9.81)
1.2/9.81 = m

F = m(v^2/r)
1.2 = (0.102 (v^2))/(0.0.75)and got 1.06 ms^-1

And for B) I couldn't understand...

 

[Doc Al]

I first tried setting up a FBD to make it clear,

Describe your FBD. What forces act on the bob?

and then after for question B, I simply used F = ma to find the mass, then after finding the mass, the speed:

F = ma
1.2 = m(9.81)
1.2/9.81 = m

The tension force does not equal the bob's weight. (You are given the bob's weight.)

F = m(v^2/r)
1.2 = (0.102 (v^2))/(0.0.75)and got 1.06 ms^-1

The tension force does not equal the centripetal force.

 

[kissafilipino]

Describe your FBD. What forces act on the bob?


The tension force does not equal the bob's weight. (You are given the bob's weight.)


The tension force does not equal the centripetal force.

1) Well it is basically, force normal, force tension and force gravity. Since centripetal can't be counted as a force, I can't count it in the FBD.
Therefore it would the FBD would have a longer normal force + tension force, and the force of gravity is shorter.


2) Hmm, your right, it doesn't equal the bobs weight, so wouldn't that mean you have to find the mass through gravity from FIRST inputing the 1.0 N pendulum weight?

and to find tension force I'd have to first use the 0.075 m rope radius, and then use F= m(v^2/r)? r = 0.075, and the pendulum weight I found earlier for m? and the 1.2 velocity for v in order to find F?

 

[Doc Al]

1) Well it is basically, force normal, force tension and force gravity. Since centripetal can't be counted as a force, I can't count it in the FBD.
Therefore it would the FBD would have a longer normal force + tension force, and the force of gravity is shorter.

There's no normal force here. The only forces on the bob are the string tension and gravity.

2) Hmm, your right, it doesn't equal the bobs weight, so wouldn't that mean you have to find the mass through gravity from FIRST inputing the 1.0 N pendulum weight?

Yes. Use the weight of the pendulum to find its mass.

and to find tension force I'd have to first use the 0.075 m rope radius, and then use F= m(v^2/r)? r = 0.075, and the pendulum weight I found earlier for m? and the 1.2 velocity for v in order to find F?

The tension and weight are given; use them to find the centripetal force. Then use the centripetal force to find the speed.

 

[rwisz]

a) Your approach is correct. Using the equations F = ma and F = m(v^2/r), we can solve for the speed of the bob at the bottom of the swing.

b) To determine the maximum height the bob will swing, we can use the conservation of energy principle. At the bottom of the swing, all of the energy is in the form of kinetic energy (KE = 1/2 mv^2). At the highest point, all of the energy is in the form of potential energy (PE = mgh).

Therefore, we can set KE at the bottom equal to PE at the top:

1/2 mv^2 = mgh

We can cancel out the mass on both sides, and solve for h:

v^2 = 2gh

h = v^2/2g

Substituting in the values we found in part a), we get:

h = (1.06 m/s)^2 / 2(9.81 m/s^2) = 0.057 m = 5.7 cm

Therefore, the maximum height the bob will swing is approximately 5.7 cm. This assumes no air resistance or friction, so in reality the height may be slightly lower.