APPLYING NEWTON’S LAWS

Weight

• Weight is a measure of the gravitational force on Earth.
• To calculate the weight of an object on Earth, use the equation:

weight = mass x acceleration due to gravity

F_w = mg

F_w = weight m = mass g = 9.8 m/s²

Sample Problem 1

An astronaut with mass 75 kg travels to Mars. What is his weight

a. On Earth?

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m = 75 kg

g = 9.8 m/s²

F_w = ?

F_w = mg

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F_w = (75)(9.8)

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F_w = 735 N

Sample Problem 1

An astronaut with mass 75 kg travels to Mars. What is his weight

b. What is his weight on Mars where g = 3.8 m/s²?

m = 75 kg

g = 3.8 m/s²

F_w = ?

F_w = mg

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F_w = (75)(3.8)

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F_w = 285 N

Sample Problem 1

An astronaut has a mass of 75 kg.

c. What is the value of g on top of a mountain if the astronaut weighs 683 N?

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m = 75 kg

g = ?

F_w = 683

F_w = mg

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683 = 75g

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683/75 = g

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g = 9.11 m/s²

Apparent Weight

• Apparent weight is the sensation of having a different weight due to the forces acting on you
• A common example of apparent weight is riding in an elevator

Apparent Weight

Tension

• Tension is a pulling force, such as by a rope or a cord
• Remember: net force = 0 when the object is at equilibrium (not moving or at constant velocity)

Sample Problem 2

A block of mass 5 Kg is suspended by a string to a ceiling and is at rest. Find the force F_t exerted by the ceiling on the string.

F_g

F_T

m = 5 kg

F = ma

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F_w = (5)(-9.8)

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F_w = -49 N

F_net = F_w + F_T

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0 = -49 + F_T

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F_T = 49 N

Spring Force: Hooke’s Law

• An ideal spring has an equilibrium length
• If a spring is stretched, then a force proportional to the increase in length is pulling inward
• If a spring is compressed, then a force proportional to the decrease in length is pushing outward

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Spring Force: Hooke’s Law

• This proportional constant is called k
• F_spring = force exerted on the spring
• ∆x = the amount the spring stretches

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Sample Problem 3

A spring was at its resting position (equilibrium) where it is attached to a wall at its left side with a block at its right side. k = 25 N/m. The block is moved leftward and the spring is displaced from .25m to .2 m. What is the spring force exerted on the bock?

k = 25 N/m

x_i = .25 m

x_f = .2 m

∆x = x_f – x_i

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∆x = .2 – .25

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∆x = -.05 m

F_spring = -k∆x

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F_spring = (-25)(-.05)

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F_spring = 1.25 N