A block with mass m is placed against a spring (with spring constant k) on a frictionless plane inclined with angle θ with respect to the horizontal. The block is not attached to the spring, but the spring is initially compressed by Δx from equilibrium. The block is then released and moves a distance d >Δx up the incline before momentarily coming to the stop. Which statements about the change in the spring potential energy ΔUs and change in the mechanical energy ΔEmech of the system are correct?

a.ΔEmech = 0
b.ΔUs < 0
c.ΔEmech < 0
d.ΔUs = 0
e.ΔEmech> 0
f.ΔUs > 0

b.

e.

Explanation:

We are given that

Spring constant=k

Angle=

Mass=m

Distance=d

Distance=

Initial potential energy of spring=

Final potential energy of spring=0

Final potential energy  of system=mgd

Initial mechanical energy of system=Initial K.E+Initial P.E=0+0=0

Final mechanical energy of the system=Kinetic energy+Potential energy=0+mgd

>0

Option b and e are true.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.