Problem 1. Crate on a Truck A truck slows down with constant acceleration from a

ID: 1584478 • Letter: P

Question

Problem 1. Crate on a Truck A truck slows down with constant acceleration from a speed v70km/h The static friction coefficient between the flad bed of the truck and the crate is 0.30 and the kinetic friction coeflicient 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 ar of the truck. (This is called the absolute accel- eration, since it is the acceleration as sen from a person at rest on the side of the road 1.3 Find the absolute acceleration ac of the crate. (Note: It might be slip ping, bearing in mind the answer in question 11. In that case the only force in -axis direction would be the kinetic friction) The absolute acceleration ac of the crate can be expressed as ac ac/T+aT, where acir is the acceleration of the crate relative to the truck and ar is the absolute acceleration of the truck 1.4 Find by use of the formula ac = ac/T + aT the acceleration of the crate relative to the truck The motion of the crate in the back of the truck is motion with constant acceleration, and hence it can be described by CIT since the velocity of the crate relative to the truck is zero when the truck driver hits the brake. In the equation vc/r denotes the velocity of the crat

Explanation / Answer

Part 1.1:

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

that is,

acceleration, a < 0.3*9.81 = 2.943 m/sec2

u = 70 km/h = 19.44 m/sec

v = 0

v2 = u2 + 2aS

S = (0 - 19.442)/(2*(-2.943))

Minimum stopping distance of the truck, S = 64.2 m

Part 1.2:

aT = ?

S = 50 m

v2 - u2 = 2aS

aT = (0 - 19.442)/(2*50)

Acceleration of the Truck, aT = -3.77 m/sec2

Part 1.3:

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

frictional force, Ff = m*g*0.3 = (2.943*m) N

Therefore,

m*aC = m*aT - Ff

aC = 3.77 - 2.943

Absolute acceleration of the Crate, aC = 0.827 m/sec2

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Problem 1. Crate on a Truck A truck slows down with constant acceleration from a

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