Question
If the mass of the pendulum bob is doubled, predict the change in kinetic energy.
Responses
A It remains constant.It remains constant.
B It is double the orginal KE.It is double the orginal KE.
C It is one-half the original KE.It is one-half the original KE.
D It is four times the orginal KE.
Responses
A It remains constant.It remains constant.
B It is double the orginal KE.It is double the orginal KE.
C It is one-half the original KE.It is one-half the original KE.
D It is four times the orginal KE.
Answers
GPT-4o mini
The kinetic energy (KE) of an object is given by the formula:
\[
KE = \frac{1}{2} mv^2
\]
where \( m \) is the mass of the object and \( v \) is its velocity.
If the mass of the pendulum bob is doubled (let's denote the original mass as \( m \) and the new mass as \( 2m \)), the kinetic energy of the bob with the new mass becomes:
\[
KE' = \frac{1}{2} (2m) v^2 = m v^2
\]
If the velocity remains unchanged, we can see that:
\[
KE' = 2 \left(\frac{1}{2} mv^2\right) = 2KE
\]
Thus, the new kinetic energy will be twice the original kinetic energy.
The correct response is:
**B It is double the original KE.**
\[
KE = \frac{1}{2} mv^2
\]
where \( m \) is the mass of the object and \( v \) is its velocity.
If the mass of the pendulum bob is doubled (let's denote the original mass as \( m \) and the new mass as \( 2m \)), the kinetic energy of the bob with the new mass becomes:
\[
KE' = \frac{1}{2} (2m) v^2 = m v^2
\]
If the velocity remains unchanged, we can see that:
\[
KE' = 2 \left(\frac{1}{2} mv^2\right) = 2KE
\]
Thus, the new kinetic energy will be twice the original kinetic energy.
The correct response is:
**B It is double the original KE.**