Question

FIND MEFIND V AT THE FIRST HILLFIND HEIGHT OF THE SECOND HILLFIND V AT POINT A

Answer 1

1)

At the starting point, the spring releases potential energy which is converted to kinetic energy of the truck. The formula fr calculating the elastic potential energy of the spring is expressed as

PE = 1/2kx^2

where

x is the extension of the spring

k is the spring constant

From the information given,

k = 8500

x = 7

Thus,

PE = 1/2 x 8500 x 7^2 = 208250 J

Since elastic potential energy of spring = kinetic energy of the truck, it means that

Kinetic energy = 208250

The formula for calculating kinetic energy is expressed as

KE = 1/2mv^2

where

m = mass of truck

v = velocity of truck

From the diagram,

m = 600

Thus,

208250 = 1/2 x 600 x v^2

208250 = 300v^2

v^2 = 208250/300 = 694.17

v = square root of 694.17

v = 26.35 m/s

The velocity at which the truck is moving is 26.35 m/s

The potential energy of the truck at that point is calculated by apply the formula,

Potential energy = mgh

where

g = acceleration due to gravity and its value is 9.81 m/s

h is the height of the truck and it is 20

m is the mass of the truck and it is 600

Thus,

Potential energy = 600 x 9.81 x 20 = 117720

Mechanical energy = potential energy + kinetic energy

Mechanical energy = 208250 + 117720 = 325970 J