Acord is used to vertically lower an initially stationary block of mass m = 9.1 kg at a constant downward acceleration of g/9. when the block has fallen a distance d = 4.6 m, find (a) the work done by the cord's force on the block, (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block. (note : take the downward direction positive)

(a) -364.64 J

(b) +410.2 J

(c) 45.58 J

(d) 3.17 m/s

Explanation:

We apply Newton's second law:

∑F = m*a (Formula 1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Data:

m= 9.1 kg

ay= g/9 m/s²

g = 9.81m/s² : acceleration due to gravity

W= m*g :  Block weight

W= m*g =9.1 kg*9.8 m/s²= 89.18 N

d= 4.6 m

Problem development

We apply the formula 1 to calculate the cord's force on the block,(T):

∑Fy = m*ay

W-T = m*g/9

W-T = W/9

T = W-W/9=(8/9) W= (8/9) *89.18 = 79.27 N

(a) Work done by the cord's force on the block (Wc)

Wc= - T*d =  - 79.27 N*4.6 m = - 364.64 J

The work ,Wc, is negative because the force (T) goes in the opposite direction to the block displacement.

(b)Work done by the gravitational force on the block(Wb)

Wb = W*d= 89.18 N*4.6 m = +410.2 J

The work ,Wb , is positive because the force (W) goes in the same direction as the block displacement

(c) kinetic energy of the block (K)

K =( 1/2)*m*v²  

v² = v₀²+2*a*d   ,v₀=0 , v²=2*a*d= 2*(g/9)* 4.6

K= ( 1/2)* 9.1* 2*(9.8/9)* 4.6 = 9.1* (9.8/9)* 4.6= 45.58 J

(d) the speed of the block.(v)

v²=2*a*d= 2*(g/9)* 4.6= 2*(9.8/9)* 4.6

v= 3.17 m/s

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.