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
