Question

A 1800-kg Jeep travels along a straight 500-m portion of highway (from A to B) at a constant speed of 10 m/s. At B, the Jeep encounters an unbanked curve of radius 50 m. The Jeep follows the road from B to C traveling at a constant speed of 10 m/s while the direction of the Jeep changes from east to south

a) What is the magnitude of the acceleration of the Jeep as it travels from A to B?
b) What is the magnitude of the acceleration of the Jeep as it travels from B to C?
c) What is the magnitude of the frictional force between the tires and the road as the Jeep negotiates the curve from B to C2

Answer 1

The magnitude of the acceleration of the Jeep from A to B is 2 m/s^2, the magnitude of the acceleration from B to C is 2 m/s^2, and the magnitude of the frictional force between the tires and the road as the Jeep negotiates the curve from B to C is 3600 N.

Step-by-step explanation:

a) The magnitude of acceleration of the Jeep as it travels from A to B can be found using the equation:
a = v^2 / r
Where v is the velocity and r is the radius of the curve.
Given that the velocity of the Jeep is 10 m/s and the radius is 50 m, the magnitude of acceleration is:
a = (10 m/s)^2 / 50 m = 2 m/s^2

b) The magnitude of acceleration of the Jeep as it travels from B to C can also be found using the same equation:
Given that the velocity of the Jeep is 10 m/s and the radius is 50 m, the magnitude of acceleration is:
a = (10 m/s)^2 / 50 m = 2 m/s^2

c) The magnitude of the frictional force between the tires and the road as the Jeep negotiates the curve from B to C can be found using the equation:
F = m * a
Where F is the frictional force, m is the mass of the Jeep, and a is the acceleration.
Given that the mass of the Jeep is 1800 kg and the acceleration is 2 m/s^2, the magnitude of the frictional force is:
F = 1800 kg * 2 m/s^2 = 3600 N