A 8000N car is traveling 12 m/s along a horizntal road when the brakes are applied. The car skids to a stop in 4.0s. How much kinetic energy does the car have.
my work:
W= 8000N/9.18m/s
mass= 815.49 kg
Kinetic energy= (1/2mv^2-1/2mv^2)
kinetic energy=1/2 (815.49)(0)^2 - 1/2 (815.49)(12 m/s)^2 =5.0 X 10^4 J
Does this seem right
I think the issue is number of significant digits. Taking it to two, I get 5.8 If you use the 8000 as one sig digit, the answer is 6*10^4 J.
so I have the right idea
but the wrong answer?
Yes, you have the right idea. Your calculations are mostly correct. However, there seems to be a misunderstanding in your work when you calculated the work done by dividing 8000N by 9.18m/s. The unit for work is Joules (J), not Newtons per meter (N/m). So, the correct calculation for the work done would be:
Work (W) = force (F) × distance (d)
W = 8000N × 12m
W = 96000 J
To calculate the kinetic energy (KE) of the car, you can use the formula:
KE = (1/2) × mass (m) × velocity (v)^2
KE = (1/2) × 815.49kg × (12m/s)^2
KE = 58901.76 J
Rounded to two significant digits, the kinetic energy of the car is approximately 59000 J.
It seems like you have the right idea in calculating the kinetic energy of the car. However, there are a few corrections and explanations that I can provide to further clarify the solution.
First, let's address the calculation of the car's mass. You mentioned using the formula W = mg, where W represents the weight of the car (8000 N) and g is the acceleration due to gravity (approximately 9.8 m/s^2). However, in this case, you should use the formula W = ma, where W is the net force acting on the car (8000 N), and a is the acceleration of the car.
Therefore, the equation becomes:
8000 N = ma
To solve for the mass (m), we need the value of acceleration. In this scenario, since the car is skidding to a stop, the acceleration is the deceleration due to the braking. To find the deceleration, we can use the formula v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (12 m/s), a is the deceleration, and t is the time taken to stop (4.0 s).
Using this equation, we rearrange to solve for deceleration (a):
0 m/s = 12 m/s + (a)(4.0 s)
Simplifying the equation, we have:
-12 m/s = 4.0s(a)
Therefore, the deceleration (a) becomes:
a = -12 m/s / 4.0 s
a = -3.0 m/s^2
Now, substituting this deceleration value (a) back into the equation to find the mass (m):
8000 N = m(-3.0 m/s^2)
To isolate the mass, we divide both sides of the equation by -3.0 m/s^2:
8000 N / -3.0 m/s^2 = m
m ≈ -2666.67 kg
Note that the negative sign indicates that the force and acceleration are in opposite directions.
Now that we have the correct mass of the car (approximately -2666.67 kg), we can calculate the kinetic energy using the formula:
Kinetic Energy = (1/2)mv^2
Plugging in the values:
Kinetic Energy = (1/2)(-2666.67 kg)(12 m/s)^2
Kinetic Energy ≈ 159999.96 J
Rounding to two significant digits, we would have:
Kinetic Energy ≈ 1.6 × 10^5 J
Therefore, the correct answer for the kinetic energy of the car is approximately 1.6 × 10^5 J.