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- Direct Change in the Centripetal Force

Lab discussion Answers to the questions Compare the dynamic force (calculated force) with the static force (measured force) for trial do they agree within the limits of experimental uncertainty?

SOLUTION

To compare we need to compute the error

The measured value is 0.6783% more than the calculated value

b) Compare the results of trial 2 in the same manner

SOLUTION

To compare we need to compute the error

The measured value is 18.8793% less than the calculated value

c) Compare the results of trial 3 in the same manner

SOLUTION

To compare we need to compute the error

The measured value is 0.4324% less than the calculated value

2. Using the results of your error analysis, which variable(s) should be measured more accurately to get a more accurate results for F

SOLUTION

i) Radius; one reason for differences is that the center of mass of the pendulum bob may not be at the physical center of the bob. Therefore, the measured length of the pendulum may not be correct.

ii) We are not taking into account the mass or rotational inertia of the pendulum rod or the force sensor. This would cause the theoretical value to have too low an estimate of the mass, making the theoretical value lower.

iii) There is friction in the Rotary Motion Sensor but this does not affect the comparison since the velocity is being measured at the lowest point, at the same place the force is being measured.

iv) There is also uncertainty in the measured length of the pendulum.

3. When the mass is hanging straight down and rotating smoothly, what are the actual physical forces acting on the mass? Draw a vector diagram and explain each force

SOLUTION

Forces acting on the mass are;

i) Gravitational force; Gravitational force gives weight to physical objects (pendulum) and causes them to fall toward the ground when dropped. gravity that will accelerate it back toward the equilibrium position

ii) Force of inertia; this force makes the pendulum swing straight out.

iii) Air Resistance ; Makes the pendulum swing in shorter arcs, but still straight arcs.

4. In this experiment, does changing only the radius change the centripetal force? Explain your answer. Does changing the radius change the velocity of the bob? Does changing only the mass cause the centripetal force to change?

SOLUTION

The centripetal force is given as;

The velocity is given as

Now it is clear that changing the radius only results to a direct change in the centripetal force (i.e. an increase in radius results to an increase in the centripetal force). This is because the centripetal force, , is directly proportional to the radius, . Similarly a change in the radius results to a change in the velocity of the bob (the two variables, , are directly proportional to each other). Lastly, changing mass only also results to a change in the centripetal force since the force and mass are directly proportional to each other.

SOLUTION

To compare we need to compute the error

The measured value is 0.6783% more than the calculated value

b) Compare the results of trial 2 in the same manner

SOLUTION

To compare we need to compute the error

The measured value is 18.8793% less than the calculated value

c) Compare the results of trial 3 in the same manner

SOLUTION

To compare we need to compute the error

The measured value is 0.4324% less than the calculated value

2. Using the results of your error analysis, which variable(s) should be measured more accurately to get a more accurate results for F

SOLUTION

i) Radius; one reason for differences is that the center of mass of the pendulum bob may not be at the physical center of the bob. Therefore, the measured length of the pendulum may not be correct.

ii) We are not taking into account the mass or rotational inertia of the pendulum rod or the force sensor. This would cause the theoretical value to have too low an estimate of the mass, making the theoretical value lower.

iii) There is friction in the Rotary Motion Sensor but this does not affect the comparison since the velocity is being measured at the lowest point, at the same place the force is being measured.

iv) There is also uncertainty in the measured length of the pendulum.

3. When the mass is hanging straight down and rotating smoothly, what are the actual physical forces acting on the mass? Draw a vector diagram and explain each force

SOLUTION

Forces acting on the mass are;

i) Gravitational force; Gravitational force gives weight to physical objects (pendulum) and causes them to fall toward the ground when dropped. gravity that will accelerate it back toward the equilibrium position

ii) Force of inertia; this force makes the pendulum swing straight out.

iii) Air Resistance ; Makes the pendulum swing in shorter arcs, but still straight arcs.

4. In this experiment, does changing only the radius change the centripetal force? Explain your answer. Does changing the radius change the velocity of the bob? Does changing only the mass cause the centripetal force to change?

SOLUTION

The centripetal force is given as;

The velocity is given as

Now it is clear that changing the radius only results to a direct change in the centripetal force (i.e. an increase in radius results to an increase in the centripetal force). This is because the centripetal force, , is directly proportional to the radius, . Similarly a change in the radius results to a change in the velocity of the bob (the two variables, , are directly proportional to each other). Lastly, changing mass only also results to a change in the centripetal force since the force and mass are directly proportional to each other.