There is a car turning on an unbanked road. The mass of the car is 2000kg moving at constant speed 36mph. The radius of the unbanked curve is 100m. the driver sees an obstacle at 20m ahead along the curve. he presses the brakes and expects to have a constant deceleration along the curve to stop just before he hits the obstacle.
what is the deceleration that the car would have if it didn't start to slide?
what is the tangential component of the acceleration
what is the normal component of accleraton
what is the magnitude of the static friction force
a, deacceleration:
vf^2=vi^2 + 2ad solve for a
b. same as a.
c. Normal=v^2/r changes in time as slowing.
d. same as c, and changes with velocity
To find the deceleration that the car would have if it didn't start to slide, we can use the centripetal acceleration formula:
a = v^2 / r
where:
a = centripetal acceleration
v = velocity of the car in m/s (converted from mph)
r = radius of the curve in meters
First, let's convert the velocity from mph to m/s:
36 mph = 36 * 0.44704 = 16.09344 m/s
Now, we can substitute the values into the formula:
a = (16.09344^2) / 100
= 259.53941 / 100
= 2.5954 m/s^2
So, the deceleration that the car would have if it didn't start to slide is approximately 2.5954 m/s^2.
Next, let's find the tangential component of acceleration. The tangential component is the component of acceleration in the direction of motion. Since the car is slowing down, it will be in the opposite direction of the velocity.
The tangential component of acceleration is equal to the negative of the magnitude of the deceleration. So, the tangential component of acceleration is -2.5954 m/s^2 (since it's slowing down).
Now, let's find the normal component of acceleration. The normal component is the component perpendicular to the direction of motion. In this case, it is equal to the centripetal acceleration.
The normal component of acceleration is equal to the magnitude of the centripetal acceleration, so it is also 2.5954 m/s^2.
Finally, let's find the magnitude of the static friction force. The static friction force is the force opposing the tendency of the car to slide. It provides the necessary centripetal force to keep the car moving in a curved path.
The magnitude of the static friction force is given by the equation:
f = m * a
where:
f = magnitude of the static friction force
m = mass of the car
a = centripetal acceleration
Substituting the known values into the formula:
f = 2000 kg * 2.5954 m/s^2
= 5190.8 N
So, the magnitude of the static friction force is approximately 5190.8 N.