Question

1.You have a 3.52 kg box sitting at the top of a 1.004 m tall frictionless ramp.

If the box is allowed to move down the ramp, what speed does it have when it has travelled 1/2 way down the ramp?

Your answer should have 2 digits after the decimal rounding rules apply.

2

You have a 1.5 kg box sitting at the top of a 3.252 m tall frictionless ramp. If the box is allowed to move down the ramp, what speed does it have when it reaches the bottom?

Your answer should have 2 digits after the decimal rounding rules apply.

Answer 1

By conservation of energy, (as only gravitational force is doing work)

Intial energy(E_i)= Final Energy(E_f)

Energy = Potentaial energy(P.E) +Kinetic energy(K.E)

----->P. E=mgh

m= mass of the object

h= height of the object from ground(reference plane)

g= acceleration due to gravity

------> K.E=mv²/2

v= speed of object

1) m=3.52kg, h=1.004m

Initial energy = Ei = mgh+mu²/2= 35.34j

Final energy =Ef =mgh/2 +mv²/2 =17.7+1.76v²

Ei=Ef

mgh=mgh/2 + mv²/2

v= 3.17m/s

2) from question (1) we got

h=3.252m

v=5.7m/s

A) speed at height h/2 = 3.17m/s

B) speed at height h/2 = 5.7 m/s

( g=10m/s2)