# A model train, with a mass of #12 kg#, is moving on a circular track with a radius of #9 m#. If the train's kinetic energy changes from #36 j# to #18 j#, by how much will the centripetal force applied by the tracks change by?

The centripetal force changes by

The centripetal force is

The kinetic energy is

The variation of kinetic energy is

The variation of centripetal force is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the change in centripetal force, we can use the relationship between kinetic energy and centripetal force.

The kinetic energy of an object moving in a circular path is given by:

[ KE = \frac{1}{2} m v^2 ]

The centripetal force acting on an object moving in a circular path is given by:

[ F_c = \frac{m v^2}{r} ]

Given: Initial kinetic energy (( KE_1 )) = 36 J Final kinetic energy (( KE_2 )) = 18 J Mass of the train (( m )) = 12 kg Radius of the circular track (( r )) = 9 m

Using the equation for kinetic energy:

[ KE_1 = \frac{1}{2} m v_1^2 ]

[ KE_2 = \frac{1}{2} m v_2^2 ]

Solving for initial and final velocities:

[ v_1 = \sqrt{\frac{2 \times KE_1}{m}} ]

[ v_2 = \sqrt{\frac{2 \times KE_2}{m}} ]

Now, calculate initial and final velocities:

[ v_1 = \sqrt{\frac{2 \times 36}{12}} = \sqrt{6} \approx 2.45 , m/s ]

[ v_2 = \sqrt{\frac{2 \times 18}{12}} = \sqrt{3} \approx 1.73 , m/s ]

Now, calculate the initial and final centripetal forces:

[ F_{c1} = \frac{m v_1^2}{r} ]

[ F_{c2} = \frac{m v_2^2}{r} ]

Substitute the values:

[ F_{c1} = \frac{12 \times (2.45)^2}{9} \approx 8.08 , N ]

[ F_{c2} = \frac{12 \times (1.73)^2}{9} \approx 4.16 , N ]

The change in centripetal force is:

[ \Delta F_c = F_{c2} - F_{c1} ]

[ \Delta F_c = 4.16 , N - 8.08 , N ]

[ \Delta F_c \approx -3.92 , N ]

Therefore, the centripetal force applied by the tracks decreases by approximately 3.92 N.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An object with a mass of #7 kg# is revolving around a point at a distance of #8 m#. If the object is making revolutions at a frequency of #9 Hz#, what is the centripetal force acting on the object?
- If a rock is thrown upward with an initial velocity of 24.5 m/s where the downward acceleration due to gravity is 9.81 m/s2. what is the rock's displacement after 1.00 s?
- How does the moon's gravity differ from earth's?
- A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #7 m#. If the train's rate of revolution changes from #1/12 Hz# to #1/3 Hz#, by how much will the centripetal force applied by the tracks change by?
- A satellite in a circular orbit 1250 kilometers above Earth makes one complete revolution every 110 minutes. What is its linear speed? (Assume that Earth is a sphere of radius 6400 kilometers.)

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7