Hello, i need help.
This is Work-Energy Theorum
A car moving at 50km/hr skids 15m with locked brakes. How far will the car skid (with locked brakes if the car moves at 100km/hr assume that the mass of the car is 500kg
Four times as far, 60 m. The mass does not matter. The kinetic energy was increased by a factor of 4. The skidding friction force stays the same.
To solve this problem, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Given:
Initial speed (v1) = 50 km/hr
Initial speed (v2) = 100 km/hr
Distance (d1) = 15 m
Mass (m) = 500 kg
First, let's find the initial kinetic energy for the car moving at 50 km/hr.
Step 1: Convert the initial speed from km/hr to m/s.
v1 = 50 km/hr * (1000 m/km) * (1 hr/3600 s) = 13.9 m/s
Step 2: Calculate the initial kinetic energy (KE1) of the car.
KE1 = 0.5 * m * v1^2
KE1 = 0.5 * 500 kg * (13.9 m/s)^2 = 96325 J
Next, let's find the final speed of the car when it moves at 100 km/hr.
Step 3: Convert the final speed from km/hr to m/s.
v2 = 100 km/hr * (1000 m/km) * (1 hr/3600 s) = 27.8 m/s
Since the car comes to a stop when skidding, the final kinetic energy (KE2) is zero.
Step 4: Apply the work-energy theorem to find the distance (d2) the car will skid at 100 km/hr.
Work done on the car = ΔKE = KE2 - KE1
0 J = KE2 - KE1
Step 5: Solve for d2.
d2 = (KE2 - KE1) / average braking force
Since the car comes to a stop, the average braking force will be the same for both cases.
Step 6: Substitute the values to find d2.
d2 = (0 J - 96325 J) / average braking force
Unfortunately, we don't have enough information to determine the average braking force. Therefore, we cannot calculate the distance (d2) the car will skid at 100 km/hr.
To solve this problem using the Work-Energy Theorem, we need to find the work done on the car to skid 15m with locked brakes when it is moving at 50km/hr. Then we can use this information to determine how far the car will skid when it is moving at 100km/hr.
First, let's convert the speed from km/hr to m/s. We know that 1 km/hr is equal to 0.2778 m/s. So, the initial speed of the car is:
50 km/hr * (0.2778 m/s / 1 km/hr) = 13.89 m/s
Next, we need to find the work done on the car. The work done can be calculated using the formula:
Work = Force * Distance
In this case, the force stopping the car is the friction force between the brakes and the road. The work done by this force is equal to the change in kinetic energy of the car.
Since the car skids with locked brakes, the initial kinetic energy is converted into work done by the friction force. Therefore, we have:
Work = Change in Kinetic Energy
The change in kinetic energy can be calculated using the formula:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Since the car comes to a stop, the final kinetic energy is zero. Therefore:
Change in Kinetic Energy = 0 - Initial Kinetic Energy
The initial kinetic energy can be calculated using the formula:
Initial Kinetic Energy = (1/2) * Mass * (Initial Speed)^2
Given that the mass of the car is 500 kg and the initial speed is 13.89 m/s, we can calculate the initial kinetic energy:
Initial Kinetic Energy = (1/2) * 500 kg * (13.89 m/s)^2 = 96418.75 J
Now, we can find the work done:
Work = 0 - 96418.75 J = -96418.75 J
The negative sign indicates that work is done against the motion of the car.
We know that the work done is equal to the force multiplied by the distance. Therefore:
Force * Distance = -96418.75 J
The force can be calculated using Newton's second law of motion:
Force = Mass * Acceleration
Since the car is skidding with locked brakes, the acceleration is negative, indicating deceleration.
Now, we can rearrange the equation to solve for distance:
Distance = -Work / Force
Substituting the values, we have:
Distance = -(-96418.75 J) / (500 kg * acceleration)
Since we know the mass of the car is 500 kg, we need to determine the acceleration. The acceleration can be calculated using the equation:
Final Velocity^2 = Initial Velocity^2 + (2 * acceleration * Distance)
Given the final velocity is 0 (since the car comes to a stop), the initial velocity is 13.89 m/s, and the distance is 15 m, we can solve for acceleration:
0 = (13.89 m/s)^2 + (2 * acceleration * 15 m)
Simplifying the equation:
0 = 192.8121 m^2/s^2 + 30 m * acceleration
Rearranging the equation, we have:
acceleration = -192.8121 m^2/s^2 / (30 m) = -6.42704 m/s^2
Now, we can calculate the distance:
Distance = -(-96418.75 J) / (500 kg * (-6.42704 m/s^2))
Simplifying the equation:
Distance = 29.996 m
Therefore, the car will skid approximately 30 meters with locked brakes when it is moving at 50 km/hr.
To find out how far the car will skid when it is moving at 100 km/hr, we will use the same process, but substitute the initial velocity of 13.89 m/s with 27.78 m/s (since 100 km/hr is double the speed of 50 km/hr).
Calculations are as follows:
Initial Kinetic Energy = (1/2) * 500 kg * (27.78 m/s)^2 = 347604.17 J
Work = 0 - 347604.17 J = -347604.17 J
Distance = -(-347604.17 J) / (500 kg * (-6.42704 m/s^2)) = 59.992 m
Therefore, the car will skid approximately 60 meters with locked brakes when it is moving at 100 km/hr.