Crate on a truck A truck slows down with constant accelerati

Crate on a truck

A truck slows down with constant acceleration from a speed v₁=70 km/h. The static friction coefficient between the flad bed of the truck and the crate is 0.30 while the kinetic friction coefficient is 0.25.

1.1 Determine the minimum stopping distance s which the truck can have if the crate is not to slip forward at all.

A cat runs across the road, and the truck comes to stop from 70 km/h in a distance of 50 m with constant acceleration.

1.2 Find the acceleration a_T of the truck. (This is called the absolute acceleration, since it is the acceleration as seen from a person at rest on the side of the road).?

1.3 Find the absolute acceleration a_C of the crate. (Note: It might be slipping, bearing in mind the answer in question 1.1. In that case the only force in x-axis direction would be the kinetic friction).

Solution

A. If crate cannot be slip then the acceleration should not be greater than 0.3*g

a < 0.3*9.81 = 2.943 m/sec^2

u = 70 km/h = 19.44 m/sec

v = 0

v^2 = u^2 + 2aS

S = (0 - 19.44^2)/(2*(-2.943))

S = 64.2 m

B.

aT = ?

S = 50 m

v^2 - u^2 = 2aS

aT = (0 - 19.44^2)/(2*50)

aT = -3.77 m/sec^2

C. Now we know that

Inertia force = m*aT = (3.77*m) N

force of friction = mg*0.3 = (2.943*m) N

Then

m*aC = m*aT - Ff

aC = 3.77 - 2.943 = 0.827 m/sec^2