A car does 8.0 ✕ 104 J of work in traveling 2.7 km at constant speed. What was the average retarding force (from all sources) acting on the car?
sorry 8.0*10^4 J of work
Force * 2700 meters = 80,000 Joules
Force = 80/2.7 Newtons
To find the average retarding force acting on the car, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy. The work done can be calculated as the product of the force applied and the distance covered.
Given:
Work done (W) = 8.0 × 10^4 J
Distance (d) = 2.7 km
First, we need to convert the distance to meters, as the SI unit of work is the Joule (J):
1 km = 1000 m
Therefore, the distance covered is:
Distance (d) = 2.7 km × 1000 m/km = 2700 m
Using the work-energy principle, we have:
Work done (W) = Change in kinetic energy (ΔKE)
Since the car is traveling at a constant speed, there is no change in kinetic energy, so ΔKE is zero. Therefore:
Work done (W) = 0
However, in this case, the work done is against the retarding force. So, we need to consider a negative sign for the work done:
Work done (W) = -|W|
Hence:
-|W| = 8.0 × 10^4 J
The force (F) can be calculated using the formula:
Work done (W) = Force (F) × Distance (d)
-|W| = F × d
Rearranging the equation to solve for the force:
F = -|W| / d
Substituting the given values:
F = -8.0 × 10^4 J / 2700 m
Calculating this expression:
F ≈ -29.63 N
Therefore, the average retarding force acting on the car is approximately -29.63 N. Note that the negative sign indicates that the force is acting in the opposite direction to the car's motion.
To find the average retarding force acting on the car, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy.
The work done by the car can be calculated using the formula:
Work = Force × Distance
Here, the work done is given as 8.0 × 10^4 J, and the distance traveled is given as 2.7 km. We need to convert the distance to meters since the SI unit of work is J (Joules).
1 km = 1000 meters
So, converting 2.7 km to meters:
Distance = 2.7 km × 1000 m/km = 2700 m
Now, we can rearrange the formula to solve for force:
Force = Work / Distance
Substituting the given values:
Force = 8.0 × 10^4 J / 2700 m
Force ≈ 29.63 N
Therefore, the average retarding force acting on the car (from all sources) is approximately 29.63 Newtons.