Amotorvehicle of mass 1200kg is travelling along alevel road at 54km/hr.The breaks are then applied and the speed of the vehicle reduced to 18km/hr over adistance of 50M .if the afriction motion resistant is constant at 160N .calculate the effective
To calculate the effective force used to slow down the vehicle, we need to consider the change in kinetic energy and the work done against friction.
First, let's calculate the initial kinetic energy of the vehicle:
The initial speed of the vehicle is 54 km/hr. We need to convert it to m/s.
Speed in m/s = (54 km/hr) * (1000 m/1 km) * (1 hr/3600 s) = 15 m/s
Kinetic energy (K.E.) = (1/2) * mass * (speed)^2
K.E. = (1/2) * 1200 kg * (15 m/s)^2
K.E. = 1/2 * 1200 kg * 225 m^2/s^2
K.E. = 135,000 J
Next, let's calculate the final kinetic energy of the vehicle:
The final speed of the vehicle is 18 km/hr. We need to convert it to m/s.
Speed in m/s = (18 km/hr) * (1000 m/1 km) * (1 hr/3600 s) = 5 m/s
K.E. = (1/2) * mass * (speed)^2
K.E. = (1/2) * 1200 kg * (5 m/s)^2
K.E. = 1/2 * 1200 kg * 25 m^2/s^2
K.E. = 15,000 J
The change in kinetic energy is:
Change in K.E. = final K.E. - initial K.E.
Change in K.E. = 15,000 J - 135,000 J
Change in K.E. = -120,000 J
The work done against friction is equal to the change in kinetic energy:
Work = -120,000 J
The work done is equal to the force of friction multiplied by the distance:
Work = force of friction * distance
-120,000 J = force of friction * 50 m
Now, let's rearrange the equation to solve for the force of friction:
force of friction = -120,000 J / 50 m
force of friction = -2,400 N (Note that the negative sign indicates that the force of friction acts in the opposite direction of motion)
Finally, to calculate the effective force, subtract the constant frictional force:
Effective force = force of friction - frictional motion resistance
Effective force = -2,400 N - 160 N
Effective force = -2,560 N (Again, the negative sign indicates the force acts in the opposite direction of motion)
Therefore, the effective force used to slow down the vehicle is -2,560 N.