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A 1500 kg car starts from rest and drives around a flat 50-m-diameter circular track. The forward force provided by the car鈥檚 drive wheels is a constant 1000 N.
a. What are the magnitude and direction of the car鈥檚 acceleration at t = 10 s? Give the direction as an angle from the r-axis.
b. If the car has rubber tires and the track is concrete, at what time does the car begin to slide out of the circle?

Short Answer

Expert verified

a) Acceleration is 1.9 m/sec2 at 21o from r axis.

b) Car will start sliding after 8.25 sec

Step by step solution

01

Part(a) Step 1: Given information

Mass of the car, m=1500 kg
Diameter of the circular track, d=50 m
The forward force, F=1000 N
Time, t=10 sec

02

Part(a) Step 2: Explanation

We can calculate tangential acceleration as

at =F/M 鈥︹︹..................(1)

Where F= forward force, m = mass of the car
And we can calculate radial acceleration as

arad =v2/r 鈥︹︹...............(2)

Where v=velocity, r = radius of the track

We can calculate acceleration

a=at2+ar2

and angle of acceleration is

=tan-1(atar)

Substitute the value to get tangential acceleration in (1)

at=1000N1500kg=0.66m/s2

Velocity of the car after 10 sec is

v=0+(0.66m/s2)10s=6.6m/s

Similarly get radial acceleration by substituting values in (2)

role="math" localid="1649086630580" ar=(6.6m/s)225m=1.77m/s2

Now calculate acceleration

a=(at2+ar2)=(0.66m/s2)2+(1.77m/s2)2=1.9m/s2

Direction of acceleration is

(the angle is)

=tan-1(0.66m/s21.77m/s2)=21o

03

Part(b) Step 1 : Given information

Mass of the car, m=1500 kg
Diameter of the circular track, d=50 m
The forward force, F=1000 N
Time, t=10 sec

04

Part(b) Step 2 : Explanation

First calculate the velocity of the car using

mv2r=mgv=rg

Substitute the values we get

v=(25m)(9.8m/s2)=15.67m/s

The car will start to slide when the final velocity v will become 0

v=u+atSubstitutevalues0=15.67m/sec-(1.9m/s2)tsolvefortt=8.25sec

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