Kinetic Energy/Forces problem

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In summary, a car and driver weighing 5490 N approach a "Bridge Out" sign and must decelerate at a rate of 10.9 m/s2 to avoid diving into the water. Using the given information and equations for kinetic energy, frictional force, and work, we can calculate the mass of the car and driver, the force of friction, and the work done to stop the car in time.
  • #1
kza62
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Homework Statement


A car and driver weighing 5490 N passes a sign stating “Bridge Out 29.3 m Ahead.”
She slams on the brakes, and the car decelerates at a constant rate of 10.9 m/s2.
The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the work done stopping the car if the car just stops in time to avoid diving into the water?
Answer in units of J.


Homework Equations


KE = 1/2mv^2
Ff = u * FN
FN = mg
F = ma


The Attempt at a Solution


Given:
a = -10.9
Fg = 9.8

need help in setting this problem up... I've never seen something weigh in N before is that important or relevant in any way? would I plug that into F = ma to find mass?
help please!
 
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  • #2
If the weight is 5490 N, can you find the mass of the person+car ?

If the deceleration is -10.9 m/s2 , can you get the force of friction acting on the car?

If you have the frictional force, can you find the work done by this force given the distance?
 
  • #3


I can help you with this problem by providing a step-by-step approach to solving it. First, let's define the known variables and the problem we are trying to solve.

Known variables:
- Mass of the car and driver (m): 5490 N
- Acceleration due to gravity (g): 9.8 m/s^2
- Initial velocity (v0): 0 m/s (since the car is at rest initially)
- Final velocity (vf): unknown
- Acceleration (a): -10.9 m/s^2 (negative because the car is decelerating)
- Distance (d): 29.3 m

Problem:
What is the magnitude of the work done stopping the car?

Step 1: Determine the final velocity of the car. To do this, we can use the kinematic equation: vf^2 = v0^2 + 2ad. Plugging in the known values, we get:
vf^2 = 0 + 2(-10.9)(29.3)
vf^2 = -638.54
vf = -25.26 m/s (negative because the car is decelerating)

Step 2: Calculate the kinetic energy of the car before braking. We can use the formula KE = 1/2mv^2, where m is the mass of the car and v is the initial velocity. Plugging in the known values, we get:
KE = 1/2 * 5490 * (0)^2
KE = 0 J

Step 3: Calculate the work done by the braking force. The work done is equal to the change in kinetic energy, which is the difference between the initial kinetic energy and the final kinetic energy. So, we can use the formula W = KEf - KEi. Plugging in the known values, we get:
W = 1/2 * 5490 * (-25.26)^2 - 0
W = 346,789.86 J

Therefore, the magnitude of the work done stopping the car is 346,789.86 J. This means that the braking force applied by the car's brakes was able to remove 346,789.86 joules of energy from the car, causing it to come to a stop just in time to avoid diving into the water.
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object, and is represented by the equation KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

2. How is kinetic energy related to forces?

Kinetic energy is related to forces through the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. This means that when a force acts on an object, it can change its velocity and therefore its kinetic energy.

3. How can I calculate the kinetic energy of an object?

To calculate the kinetic energy of an object, you will need to know its mass and velocity. You can then use the equation KE = 1/2 * m * v^2 to find the kinetic energy in joules (J).

4. Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy, such as potential energy or thermal energy. For example, when a moving object collides with another object, its kinetic energy may be converted into sound or heat energy.

5. What is the difference between kinetic energy and potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object possesses due to its position or state. Kinetic energy is related to an object's velocity, while potential energy is related to its height or location in a gravitational field.

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