Question

The kinetic energy K of a moving object varies jointly with its mass m and the square of its velocity v. If an object weighing 40 kilograms with a velocity of 15 meters per second has a kinetic energy of 1000 joules, find the kinetic energy if the velocity is increased to 20 meters per second. Round your answer to two decimal places.

Answer 1

Answer:

K' = 1777.777  J

Explanation:

Given that

m = 40 kg

v= 15 m/s

K=1000

Given that kinetic energy(K) varies with mass(m) and velocity(v)

 K= C(mv²)

Where

C= Constant

m=mass

v=velocity

When

m = 40 kg ,v= 15 m/s ,K=1000

 K= C(mv²)

1000 = C( 40 x 15²)

C=0.111111

When m = 40 kg and v= 20 m/s

K' = C(mv²)

K= 0.1111 x (40 x 20²)

K' = 1777.777  J

Answer 2

Answer:

1777.78 Joules

Explanation:

v = Velocity of object

m = Mass of object

Kinetic energy

$K=\frac{1}{2}mv^2\\\Rightarrow m=\frac{2K}{v^2}\\\Rightarrow m=\frac{2\times 1000}{15^2}$

The mass of the object is 4.44 kg.

Here the mass remains constant

If v = 20 m/s

$K=\frac{1}{2}mv^2\\\Rightarrow K=\frac{1}{2}\times\frac{2\times 1000}{15^2}\times 20^2\\\Rightarrow K=1777.78\ Joules$

The kinetic energy of the object when the speed is increased to 20 m/s is 1777.78 Joules