# What are the ways in which the mass of a body can be determined without using a laboratory balance?

##### 1 Answer

There are many equations that can be used to calculate the mass of a body. You can use the equation for **density** , the equation from **Newton's second law** of motion, the equation for **kinetic energy** , and the equation for **specific heat capacity** . Which equation you use depends on what data you have.

**DENSITY EQUATION**

The density equation is

You can use the **density equation** to calculate mass if you know the **density** and **volume** of a substance. The way to solve the density equation for mass is to multiply density x volume:

**Example.**

**Q.** What is the mass of a piece of aluminum that has a density of

**A.**

**NEWTON'S SECOND LAW:**

The equation for Newton's 2nd law is usually written as

You can use **Newton's 2nd law of motion** if you know the **force (in Newtons)** and the **acceleration** . To solve for mass, divide force by acceleration:

**Example 1. Determining the mass of a dog from its weight in Newtons.** Weight is the force in Newtons, that is caused by the gravity of the earth acting on a body's mass. The acceleration due to gravity is

**Q.** What is the mass of a dog that weighs 323 N?

**A.**

**Example 2.**

**Q.** What is the mass of a truck if it produces a force of 14,000 N while accelerating at a rate of

**A.**

**Note:** Because

**KINETIC ENERGY**

The kinetic energy (KE) equation is:

If you know KE and speed, you can use the KE equation and solve for m.

**Example.**

**Q.** What is the mass of a baseball that has a kinetic energy of 105 J and is traveling at 10 m/s?http://www.biologycorner.com/physics/energy/problemset_kinetic_potential_energy.html

**A.**

**SPECIFIC HEAT**

The equation for specific heat is

**Example.**

**Q.** The water in a swimming pool gives up

**A.**

**SUMMARY**

If you know **density** and **volume** , you would use the **density equation** to find mass.

If you know **force in Newtons** and **acceleration** , you would use the equation from **Newton's second law** to determine mass.

If you know **KE** and **speed** , you can use the **equation for KE** to calculate mass.

If you know **heat energy** gained or lost, **specific heat capacity** , and **temperature change** , you can use the **specific heat equation** to calculate mass.

There are probably more ways to calculate mass depending on what data you have. However, at the moment, these are the ones I can think of.