SOLVING PROBLEMS ON KINETIC ENERGY

Example 1 :

What is the Kinetic Energy of a 150 kg object that is moving with a speed of 15 m/s?

Solution :

K.E = (1/2)mv²

Substitute m = 150 and v = 15.

= (1/2)(150)(15)²

= (1/2)(150)(225)

= 16875

The Kinetic Energy of the object is 16875 joules.

Example 2 :

An object has a kinetic energy of 425 joules and a mass of 34 kg. How fast is the object moving?

Solution :

K.E = 425 joules

(1/2)mv² = 425

Substitute K. E = 25 and m = 34.

(1/2)(34)v² = 425

17v² = 425

Divide both sides by 17.

v² = 25

Take square root on both sides.

v = 5

The object is moving at a rate of 5 m/s.

Example 3 :

An object moving with a speed of 25 m/s and has a kinetic energy of 1875 joules. What is the mass of the object?

Solution :

K.E = 1875 joules

(1/2)mv² = 1875

Substitute v = 25.

(1/2)m(25)² = 1875

625m/2 = 1875

Multiply both sides by 2.

625m = 3750

Divide both sides by 625.

m = 6

The mass of the object is 6 kg.

Example 4 :

If the mass of an object is halved and its speed is doubled, how does the kinetic energy change?

Solution :

Let m be the mass and v be the speed of the object.

Then, the kinetic energy is

K.E = (1/2)mv²

Since the mass of is halved and its speed is doubled, replace m by (1/2)m and v by 2v.

New K.E = (1/2)(1/2)m(2v)²

= (1/2)(1/2)m(4v²)

= (1/2)m(2v²)

= 2 x (1/2)mv²

= 2 x K.E

If the mass of an object is halved and its speed is doubled, the kinetic energy is doubled.

Example 5 :

If the kinetic energy of a moving tennis ball is doubled, its velocity must have increased by what factor?

Solution :

Formula for kinetic energy.

K.E = (1/2)mv²

When the kinetic energy is doubled, let us assume that the velocity has to be increased by the factor 'x'.

2K.E = (1/2)m(xv)²

2K.E = (1/2)mx²v²

2K.E = x²(1/2)mv²

2K.E = x²K.E

Divide both sides by K.E.

2 = x²

Take square root on both sides.

√2 = x

If the kinetic energy of a moving tennis ball is doubled, its velocity must have increased by the factor √2.

Example 6 :

A radioactive element loses 15 percent of its mass and 20 percent of its velocity. By what percent has its kinetic energy decreased?

Solution :

Formula for kinetic energy.

K.E = (1/2)mv²

Since radioactive element loses 15 percent of its mass and 20 percent of its velocity, replace 'm' by '0.85m' and 'v' by '0.8v'.

New K.E = (1/2)(0.85m)(0.8v)²

= (1/2)(0.85m)(0.64v²)

= 0.544 x (1/2)mv²

= 0.544 x K.E

= 54.4 % of K.E

After 15 percent loss in mass and 20 percent loss velocity, the kinetic energy becomes 54.4% of its original level.

100% - 54.4% = 45.6%

After the radioactive element loses 15 percent of its mass and 20 percent of its velocity, the kinetic energy has decreased by 45.6%

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.