How Does Air Force Affect Kinetic Energy in a Fancart?

In summary, a fancart with a mass of 0.8 kg initially has a velocity of < 0.7, 0, 0 > m/s. When the fan is turned on, the air exerts a constant force of < -0.4, 0, 0 > N on the cart for 1.5 seconds. The change in momentum over this interval is <-0.6, 0, 0>, but the change in kinetic energy cannot be determined without knowing the initial and final kinetic energies.
  • #1
magma_saber
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0

Homework Statement


A fancart of mass 0.8 kg initially has a velocity of < 0.7, 0, 0 > m/s. Then the fan is turned on, and the air exerts a constant force of < -0.4, 0, 0 > N on the cart for 1.5 seconds.

What is the change in momentum of the fancart over this 1.5 second interval?

What is the change in kinetic energy of the fancart over this 1.5 second interval?


Homework Equations


K = 1/2mv2
K = p2/2m

The Attempt at a Solution


I got the change in momentum. It's <-.6,0,0>
I can't find the change in kinetic energy.
I tried K = 1/2mv2 and got 0.196
I also tried p2/2m and got 0.225
 
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  • #2
You must find the KE before and after. Take the difference to get the change.
 
  • #3


I can confirm that your calculation for the change in momentum is correct. However, your calculations for the change in kinetic energy are incorrect.

To find the change in kinetic energy, we can use the formula K = 1/2mv^2, where K is kinetic energy, m is mass, and v is velocity. In this case, the mass of the fancart is 0.8 kg and the initial velocity is 0.7 m/s. Plugging these values into the formula, we get:

K1 = 1/2(0.8 kg)(0.7 m/s)^2 = 0.196 J

Now, to find the final kinetic energy, we need to calculate the final velocity of the fancart. We know that the air exerts a constant force of -0.4 N on the cart for 1.5 seconds, so we can use Newton's second law (F = ma) to find the acceleration:

-0.4 N = 0.8 kg * a
a = -0.5 m/s^2

Using the equation v = u + at, where u is the initial velocity, a is acceleration, and t is time, we can find the final velocity:

v = 0.7 m/s + (-0.5 m/s^2)(1.5 s) = 0.7 m/s - 0.75 m/s = -0.05 m/s

(Note: the negative sign indicates that the velocity is in the opposite direction of the initial velocity)

Now, we can plug this final velocity into the kinetic energy formula to find the final kinetic energy:

K2 = 1/2(0.8 kg)(-0.05 m/s)^2 = 0.002 J

Finally, to find the change in kinetic energy, we can subtract the initial kinetic energy from the final kinetic energy:

ΔK = K2 - K1 = 0.002 J - 0.196 J = -0.194 J

Therefore, the change in kinetic energy of the fancart over the 1.5 second interval is -0.194 J. This means that the kinetic energy of the fancart has decreased due to the negative work done by the air on the cart.
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

2. How is the kinetic energy of a kart calculated?

The kinetic energy of a kart is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the kart and v is its velocity.

3. How does the kinetic energy of a kart affect its performance?

The kinetic energy of a kart directly affects its speed and acceleration. The higher the kinetic energy, the faster the kart can go and the quicker it can accelerate.

4. What factors can affect the kinetic energy of a kart?

The kinetic energy of a kart can be affected by its mass and velocity. Other factors such as air resistance and surface friction can also play a role in the overall kinetic energy of the kart.

5. How can the kinetic energy of a kart be increased?

The kinetic energy of a kart can be increased by increasing its mass or its velocity. However, it's important to note that increasing the mass may also affect the handling and maneuverability of the kart, while increasing the velocity may require more power and may also increase the risk of accidents.

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