A 1386 kg car traveling at 61 km/h is brought to a stop while skidding 42 m. What is the work done on the car by the frictional forces? (Use formula: v2 = vo2 + 2ad)
To find the work done on the car by the frictional forces, we first need to find the initial velocity of the car (vo), the final velocity of the car (v), and the acceleration (a).
Given:
Mass of the car (m) = 1386 kg
Initial velocity (vo) = 61 km/h
Distance (d) = 42 m
First, let's convert the initial velocity from km/h to m/s:
61 km/h = 61 * (1000 m / 3600 s) ≈ 16.94 m/s
Next, let's find the final velocity by using the formula:
v^2 = vo^2 + 2ad
Rearranging the formula, we get:
v^2 - vo^2 = 2ad
Plugging in the values, we have:
v^2 - (16.94 m/s)^2 = 2 * a * 42 m
Calculating:
v^2 - 287.23 m^2/s^2 = 84a
Now, let's determine the value of a. We know that the final velocity v is 0 because the car comes to a stop, so:
0 - 287.23 m^2/s^2 = 84a
Simplifying the equation:
-287.23 m^2/s^2 = 84a
Finally, solving for a:
a = -287.23 m^2/s^2 / 84
a ≈ -3.42 m/s^2
Now that we have the acceleration, we can find the work done by frictional forces using the work-energy principle. The work done is equal to the change in kinetic energy:
Work = ΔKE = KE_final - KE_initial
Since the car comes to a stop, the final kinetic energy (KE_final) is zero. Therefore:
Work = -KE_initial
The initial kinetic energy (KE_initial) can be calculated using the formula:
KE = 0.5 * m * v^2
Plugging in the values:
KE_initial = 0.5 * 1386 kg * (16.94 m/s)^2
Calculating:
KE_initial ≈ 158359.49 J
Therefore, the work done on the car by the frictional forces is approximately 158359.49 J.
To find the work done on the car by the frictional forces, we first need to find the initial velocity (vo), the final velocity (v), and the acceleration (a) using the provided information.
Given:
Mass of car (m) = 1386 kg
Initial velocity (vo) = 61 km/h
Final velocity (v) = 0 km/h (since the car is brought to a stop)
Distance traveled (d) = 42 m
First, let's convert the initial velocity from km/h to m/s:
vo = 61 km/h * (1000 m/1 km) * (1 h/3600 s) = 16.9 m/s
Next, we can use the formula: v^2 = vo^2 + 2ad to find the acceleration:
0^2 = (16.9 m/s)^2 + 2a * 42 m
Rearranging the equation, we get:
0 = 284.41 m^2/s^2 + 84a
Solving for a, we have:
84a = -284.41 m^2/s^2
a = (-284.41 m^2/s^2) / 84
a ≈ -3.39 m/s^2 (negative sign indicates deceleration)
Now that we have the acceleration, we can calculate the work done by frictional forces using the work-energy principle:
Work = force * distance
The force of friction can be found using Newton's second law: F = ma, where m is the mass of the car and a is the acceleration. So:
F = (1386 kg) * (-3.39 m/s^2)
F ≈ -4695.54 N (negative sign indicates opposite direction of motion)
Now we can calculate the work done:
Work = force * distance
Work = (-4695.54 N) * (42 m)
Work ≈ -197410.68 J (Joules)
Therefore, the work done on the car by the frictional forces is approximately -197410.68 Joules. The negative sign indicates that the work is done against the motion of the car.