A crate of books is to be put on a truck with the help of some planks sloping up

Question

A crate of books is to be put on a truck with the help of some planks sloping up at 35. The mass of the crate is 70 kg, and the coefficient of sliding friction between it and the planks is 0.7. You and your friends push horizontally with a force ~F .The acceleration of gravity is 9.81 m/s2 . Once the crate has started to move, how
large must F be in order to keep the crate moving at constant speed?
Answer in units of kN
if you shoves a wooden block up a rough in- cline. The block slides up, decelerates to a stop, and then slides back down the incline. You know g = 9.8 m/s2 and the angle = 35 the incline makes with the horizontal, if you don’t know the block’s mass m or the friction coefficient µ. You observe that on its way down, the block has acceleration adown = 2.9 m/s2. What was the magnitude of the blocks deceleration aup on its way up?
Answer in units of m/s2

Explanation / Answer

a) Normal reaction on the crate= F sin+ Mg cos=N

acceleration=0

   F cos - Mg sin - (Mg cos + F sin) = 0

=35° M=70 kg g= 9.81m/s2  =0.7

On substituting values and solving,

F= 1.87 kN

b) for up the plane,

-mg cos - mg sin = ma1

a1= -(g cos + g sin )= -(8.03 + 5.62)...(1)

for down the plane,

mg sin - mg cos= ma2

a2= 2.9 = gsin - g cos = 5.62- 8.02

=0.34

in (1)

a1=-( 8.03*0.34 + 5.62)

a1= -8.35 m/s2

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