A toy car has a kinetic energy of 12 J. What is its kinetic energy after a frictional force of 0.5 N has acted on it for 6 m?
12J-(0.5N*6m)=????
To find the change in kinetic energy, we need to calculate the work done by the frictional force.
The work done can be calculated using the formula:
Work (W) = Force (F) * Distance (d) * cos(θ)
Since the force and displacement are in the same direction, the angle between them is 0 degrees, and the cos(0) = 1. Therefore, we can exclude the angle in this calculation.
Given:
Force (F) = 0.5 N
Distance (d) = 6 m
Work (W) = 0.5 N * 6 m * cos(0)
Work (W) = 3 N*m
The change in kinetic energy (ΔKE) is equal to the work done by the frictional force. So, ΔKE = 3 N*m.
To find the final kinetic energy (KE_final), we need to subtract the change in kinetic energy from the initial kinetic energy (KE_initial).
Given:
Initial kinetic energy (KE_initial) = 12 J
KE_final = KE_initial - ΔKE
KE_final = 12 J - 3 N*m
KE_final = 9 J
Therefore, the final kinetic energy of the toy car after the frictional force of 0.5 N has acted on it for 6 m is 9 Joules.
To calculate the change in kinetic energy, we need to consider the work done by the frictional force. The work done on an object is given by the formula:
Work = Force * Distance * Cos(θ)
In this case, the force is the frictional force, the distance is the distance over which the force acts, and θ is the angle between the force and the direction of motion. Since the frictional force acts opposite to the direction of motion, the angle between them is 180 degrees, and the cosine of 180 degrees is -1. So the equation becomes:
Work = - (Force * Distance)
The work done by the frictional force is equal to the change in kinetic energy:
Work = Change in Kinetic Energy
So we have:
Change in Kinetic Energy = - (Force * Distance)
Plugging in the values given in the question:
Force = 0.5 N
Distance = 6 m
Change in Kinetic Energy = - (0.5 N * 6 m)
= - 3 J
Since the work done by the frictional force is negative, it means that the kinetic energy of the toy car decreases by 3 J.
Therefore, the final kinetic energy of the toy car would be:
Initial Kinetic Energy - Change in Kinetic Energy
= 12 J - 3 J
= 9 J
Hence, the final kinetic energy of the toy car after the frictional force has acted on it for 6 m is 9 J.