A racing car accelerates from 50 km per hour to 200 km per hour in 3.0 seconds along a straight track, and the acceleration is constant during this period. If the axles are 40 cm above the road, what is the magnitude of the angular acceleration of the wheels?
well, in each rotation of the wheel, the wagon goes 2PI*r
speed car=2PIr/timeforonerotation=w*r
w=speedcar/r so change those speed in km/hr to m/s, find wi and wf
angacceleration= (wf-wi)/3sec
So 200km/h is 55.5 m/s and 50km/h is 13.75 m/s.
Wi=55.5/0.4=138.75
Wf=13.75/0.4=34.36
(138.75-34.36)/3= 34.7
Thanks bob. I think this is correct, forgive my lack of units.
To find the magnitude of the angular acceleration of the wheels, we can use the relationship between linear and angular acceleration.
Given:
Initial linear velocity, u = 50 km/h
Final linear velocity, v = 200 km/h
Time, t = 3.0 seconds
Height of axles above the ground, h = 40 cm
First, let's convert the linear velocities from km/h to m/s.
1 km/h = 1000 m/3600 s = 10/36 m/s
Initial linear velocity, u = 50 km/h * (10/36) m/s = 500/36 m/s
Final linear velocity, v = 200 km/h * (10/36) m/s = 2000/36 m/s
Next, let's find the linear acceleration, a.
We can use the formula:
a = (v - u) / t
a = (2000/36 - 500/36) / 3 = (1500/36) / 3 = 125/12 m/s^2
Now, let's find the radius of the circular path by using the height of the axles above the road.
The radial acceleration, arad = g = 9.8 m/s^2 (acceleration due to gravity)
We can use the relationship between linear acceleration and radial acceleration.
arad = a / r
where r is the radius of the circular path.
We re-arrange the formula to solve for r.
r = a / arad
Substituting the values:
r = (125/12) / 9.8 = (125/12) * (1/9.8) = 125/1176 = 25/294 m
Finally, let's find the angular acceleration, α.
Using the formula:
α = a / r
α = (125/12) / (25/294) = (125/12) * (294/25) = 3675/100 m/s^2
Therefore, the magnitude of the angular acceleration of the wheels is 3675/100 m/s^2.
To find the magnitude of the angular acceleration of the wheels, we will first calculate the linear acceleration of the car using its initial and final speeds, and the time taken.
1. Convert the speeds from km/h to m/s:
Initial speed (v1) = 50 km/h = (50 * 1000) / 3600 m/s = 13.89 m/s
Final speed (v2) = 200 km/h = (200 * 1000) / 3600 m/s = 55.56 m/s
2. Calculate the linear acceleration (a) using the formula:
a = (v2 - v1) / t
where t is the time taken, which is 3.0 seconds.
a = (55.56 m/s - 13.89 m/s) / 3.0 s = 13.89 m/s^2
3. Convert the axle height from centimeters to meters:
Axle height (h) = 40 cm = 40 / 100 m = 0.4 m
4. Now, we can calculate the magnitude of the angular acceleration (α) using the formula:
α = a / r
where r is the distance between the axle and the center of rotation (in this case, the road).
Since the axle is 0.4 m above the road, the radius (r) is also 0.4 m.
α = 13.89 m/s^2 / 0.4 m = 34.725 rad/s^2
Therefore, the magnitude of the angular acceleration of the wheels is 34.725 rad/s^2.