a 1200 kg car going 30 m/s applies its brakes and skids to rest. if the friction force between the sliding ires and the pavement is 6000 N, how far does the car skid before coming to rest. I know the ans is 90 m
what work/energy formula should i use to get this answer? can you help me plug in the numbers where they belong?
To find the distance the car skids before coming to rest, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to its change in kinetic energy. In this case, the work done by the friction force in stopping the car will be equal to the initial kinetic energy of the car.
The formula we can use is:
Work done (W) = Change in kinetic energy (ΔKE)
The change in kinetic energy can be calculated using the formula:
ΔKE = 1/2 * mass * (final velocity^2 - initial velocity^2)
Given:
Mass (m) = 1200 kg
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 m/s
By substituting the given values into the above formula, we can calculate the change in kinetic energy.
ΔKE = 1/2 * 1200 kg * (0 m/s)^2 - (30 m/s)^2
Simplifying the equation, we have:
ΔKE = 1/2 * 1200 kg * (0 - 900) m^2/s^2
ΔKE = -540,000 J
Since the work done by friction force is equal to the change in kinetic energy, the work done (W) is also -540,000 J.
Now we can calculate the distance the car skids using the work-energy formula:
W = force * distance
Rearranging the formula to find the distance:
Distance (d) = W / force
Substituting the given values:
Distance (d) = -540,000 J / -6000 N
Simplifying the equation, we have:
Distance (d) = 90 m
Therefore, the car skids 90 meters before coming to rest.
To determine the distance the car skids before coming to rest, you can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the car starts with kinetic energy due to its initial velocity and ends with its kinetic energy being zero when it comes to rest.
The formula to calculate the work done on an object is:
Work = Force * Distance * cosθ
In this scenario, since the car skids in a straight line, the angle (θ) between the direction of force (friction) and the direction of motion is 0 degrees. Therefore, cos(theta) is equal to 1, and you can ignore it for now.
Now, let's plug in the given values into the formula to solve for the distance:
Work = Force * Distance
Since the work done is equal to the change in kinetic energy:
Work = ΔKE = KE_final - KE_initial
Initially, the car has kinetic energy of:
KE_initial = (1/2) * mass * (initial velocity)^2
KE_initial = (1/2) * 1200 kg * (30 m/s)^2
KE_initial = 540,000 Joules
As the car comes to rest, its final kinetic energy is zero:
KE_final = 0
Therefore, the work done on the car is equal to the initial kinetic energy:
Work = ΔKE = KE_final - KE_initial = 0 - 540,000 Joules = -540,000 Joules
Now, we can substitute the given force and solve for the distance:
Work = Force * Distance
-540,000 J = 6000 N * Distance
To isolate the distance, divide both sides of the equation by 6000 N:
-540,000 J ÷ 6000 N = Distance
Distance = -90 m
Since distance cannot be negative, we take the absolute value:
Distance = 90 m
Hence, by applying the work-energy principle and plugging in the given values into the appropriate formula, we find that the car skids a distance of 90 meters before coming to rest.
KEenergy car-friction*distance=remaining energy.
1/2 m v^2-6000*distance=0
solve for distance.