Calculate the work required to be done to stop a car of 1500kg moving with a velocity of 60km/hr?
To calculate the work required to stop a car, we need to consider the kinetic energy of the car. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
First, we need to calculate the initial kinetic energy of the car. The kinetic energy (KE) formula is given by:
KE = 0.5 * mass * velocity^2
Given:
Mass (m) = 1500 kg
Velocity (v) = 60 km/hr = 60 * (1000/3600) m/s (Converting km/hr to m/s)
Let's calculate the initial kinetic energy of the car:
KE = 0.5 * m * v^2
Substituting the given values:
KE = 0.5 * 1500 kg * (60 * (1000/3600) m/s)^2
Simplifying:
KE = 0.5 * 1500 kg * (60 * 1000/3600 m/s)^2
KE = 0.5 * 1500 kg * (60000/3600 m/s)^2
KE = 0.5 * 1500 kg * (166.67 m/s)^2
KE = 0.5 * 1500 kg * 27777.78 m^2/s^2
KE = 20833333.33 kg * m^2/s^2
The initial kinetic energy of the car is 20833333.33 kg * m^2/s^2.
To stop the car, we need to bring its velocity down to zero. This means the final kinetic energy is zero.
Now, the work done to stop the car is equal to the change in kinetic energy:
Work = Change in kinetic energy = Initial kinetic energy - Final kinetic energy = 20833333.33 kg * m^2/s^2 - 0
Therefore, the work required to stop the car is 20833333.33 kg * m^2/s^2.
To calculate the work required to stop a car, you need to consider the change in kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity^2
First, we need to convert the velocity from km/hr to m/s since the SI unit of mass is kilograms and the SI unit of velocity is meters per second.
Given:
Mass of the car, m = 1500 kg
Initial velocity of the car, v = 60 km/hr
Step 1: Convert the velocity from km/hr to m/s
Given that 1 km/hr = (1 * 1000 m) / (1 * 3600 s) = 5/18 m/s
Converting the car's velocity:
v (m/s) = 60 km/hr * (5/18) = 50/3 m/s
Step 2: Calculate the initial kinetic energy
Kinetic Energy (initial) = 0.5 * mass * velocity^2
Kinetic Energy (initial) = 0.5 * 1500 kg * (50/3 m/s)^2
Step 3: Calculate the final kinetic energy
When the car is stopped, the final velocity, v(final), is 0 m/s. Therefore, the final kinetic energy is:
Kinetic Energy (final) = 0.5 * mass * (0 m/s)^2
= 0 J (since any value multiplied by 0 is 0)
Step 4: Calculate the work done (change in kinetic energy)
The work done to stop the car is equal to the change in kinetic energy, which can be calculated as:
Work Done = Kinetic Energy (final) - Kinetic Energy (initial)
Work Done = 0 J - (0.5 * 1500 kg * (50/3 m/s)^2)
Simplifying the expression, we get:
Work Done = - 0.5 * 1500 kg * (50/3 m/s)^2
Therefore, the work required to stop the car is -125000 J (The negative sign indicates that work is being done on the car to stop it.)