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CHAPTER 12 Forces and Motion > 12.2 Newton's First and Second Laws of Motion > Newton's Second Law of Motion

A force exerted on a single shopping cart, produces greater acceleration than when the same force is applied on a chain of eight shopping carts. A set of labeled arrows indicate the direction and magnitude of force and acceleration.

Figure 13 Acceleration depends directly on force and inversely on mass. Neglecting friction, when the same force acts, the single cart accelerates eight times faster than the chain of eight carts.

Predicting How would the acceleration of a chain of two carts compare with the acceleration of a single cart if t h e same force acted on both?

The shopping carts in Figure 13 further illustrate Newton's second law. What happens if you push on a single shopping cart? The unbalanced force causes the cart to accelerate. What happens when you push with the same force on a chain of eight shopping carts? The acceleration of the chain of carts is much less than that of the single cart. The chain of carts accelerates less because it has more mass.

Weight and Mass

Do you sometimes talk about weight and mass as if they were the same thing? Although related to each other, mass and weight are not the same. Weight is the force of gravity acting on an object. An object's weight is the product of the object's mass and acceleration due to gravity acting on it.

$W e i g h t = M a s s \times A c c e l e r a t i o n d u e t o g r a v i t y = 112 k g \times 9.8 m / s^{2} = 1100 k g \cdot m / s^{2} = 1100 N$

The weight formula is basically Newton's second law. However, weight (W) is substituted for force (F) and acceleration due to gravity (g) is substitutued for acceleration (a). In other words, W = mg is a different form of $a = \frac{F}{M}$ , that is when the equation is solved for force, F = ma. The value of g in the formula is 9.8 m/s².

In using the weight formula or Newton's second-law formula, make sure you use the correct units. The force (F or W) should be in newtons, the acceleration (a or g) in meters per second squared, and the mass (m) in kilograms. The following example shows how to use the weight formula.

If an astronaut has a mass of 112 kilograms, what is his weight on Earth where the acceleration due to gravity is 9.8 m/s²?

$W e i g h t = M a s s \times A c c e l e r a t i o n d u e t o g r a v i t y = 112 k g \times 9.8 m / s^{2} = 1100 k g \cdot m / s^{2} = 1100 N$