The amount of work done can be solved using the formula:
Work = Force x Distance = Change in kinetic energy
Kinetic energy can be solved using the formula: KE = (1/2)*m*v^2
So, change in kinetic energy = (1/2)*m*(Vf)^2 - (1/2)*m*(Vo)^2
Where:
Vf = final velocity = 90 kph = 25 m/s
Vo = initial velocity = 72 kph = 20 m/s
substituting the given values:
Work = (1/2)*2500*(25^2) - (1/2)*2500*(20^2) = 281250 J, which can also be expressed as 2.8 x 10^5 Joules.
Among the choices, the correct answer is A.
Kinetic energy is calculated through the equation,
KE = 0.5mv²
At initial conditions,
m₁: KE = 0.5(0.28 kg)(0.75 m/s)² = 0.07875 J
m₂ : KE = 0.5(0.45 kg)(0 m/s)² = 0 J
Due to the momentum balance,
m₁v₁ + m₂v₂ = (m₁ + m₂)(V)
Substituting the known values,
(0.29 kg)(0.75 m/s) + (0.43 kg)(0 m/s) = (0.28 kg + 0.43 kg)(V)
V = 0.2977 m/s
The kinetic energy is,
KE = (0.5)(0.28 kg + 0.43 kg)(0.2977 m/s)²
KE = 0.03146 J
The difference between the kinetic energies is 0.0473 J.
To solve this problem, we will start by defining each of the variables given and proceed to find the modulus of elasticity of the object. We will calculate the deformation per unit of elastic volume and finally we will calculate the net energy of the system. Let's start defining the variables
Yield Strength of the metal specimen
Yield Strain of the Specimen
Diameter of the test-specimen
Gage length of the Specimen
Modulus of elasticity
Strain energy per unit volume at the elastic limit is
Considering that the net strain energy of the sample is
Therefore the net strain energy of the sample is 
If Earth was twice as far from the sun, the force of gravity attracting the Earth to the sun would be only one-quarter as strong. The correct answer will be C.
