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STE Name_____________________ Physics Intro
1. Mass, Force and Gravity
Before attempting to understand force, we need to look at mass and acceleration.
a) What does mass measure? The quantity of matter(atoms)
b) What is the ratio of atoms in the two diamonds?
0.100 kg 0.001 kg (5 carat diamond)
0.100 kg/0.001 kg = 100/1. The ratio of atoms is the mass ratio because the atoms are all identical (carbon)
c) What is the ratio of atoms if we compare the number of atoms in the big diamond to those found in 0.100 kg of gold?
Now we are comparing different atoms, so we need a mole ratio:
100g Au/197g/mole = 0.507 moles 100 g C/12 = 8.33 moles
Catoms/Au atoms =8.33/0.507 = 16.
d) If you bring the 0.100 kg diamond to Mars, where gravity is 0.38*^1 of what it is on the Earth, what will its mass be? Why?
Mass will remain constant. Same number of atoms.
e) What is acceleration?
f) The Ferrari Scuderia can go from 0 to 100 km/h (27.78 m/s) in 3.7 s. What is its acceleration?
g) Force is a push or pull equal to the product of mass and acceleration.
F = ma
A force is what’s needed to move a mass from rest to a certain speed. It is also what’s needed to decelerate (negative acceleration) a mass.
Find the force needed to accelerate a 1250 kg Scuderia from rest to 27.78 m/s in 3.7 s.
F = 1250 kg * = 9375 N
(^1) The relative gravity(gp/ge) is calculated from gp/ge = mp/rp (^2) , where mp is the planet’s relative mass and rp is
the planet’s relative size. For Mars mp =0.107 and rp= 0.532. The formula comes from Newton’s Law of Gravitation which mathematically looks like Coulomb’s Law.
mass which supposedly falls faster. This contradiction arises because the original assumption is false.
l) The product of mass and gravitational acceleration is known as weight. Weight is the gravitational force given by F = mg. If you bring the 0.1000 kg diamond to Mars, where gravity is 0.38 of what it is on the Earth, what will its weight be?
Weight on Earth Weight on Mars F = mg = 0.100(9.8) = 0.98 N
F = mgmars = 0.100(0.38)(9.8) = 0.37 N
m) How does this diagram help us realize that gravity keeps the moon in orbit?
If the earth’s gravity was not pulling the moon towards itself then the moon would keep going in a straight line, as shown in the diagram. The red arrow is the force of gravity that pulls it to its actual position along the ellipse(almost a circle).
From: http://galileoandeinstein.physics.virginia.edu/lectures/newton.html
Let us now turn to the central topic of the Principia , the universality of the gravitational force. The legend is that Newton saw an apple fall in his garden in Lincolnshire, thought of it in terms of an attractive gravitational force towards the earth, and realized the same force might extend as far as the moon. He was familiar with Galileo’s work on projectiles, and suggested that the moon’s motion in orbit could be understood as a natural extension of that theory. To see what is meant by this, consider a gun shooting a projectile horizontally from a very high mountain, and imagine using more and more powder in successive shots to drive the projectile faster and faster.
The parabolic paths would become flatter and flatter, and, if we imagine that the mountain is so high that air resistance can be ignored, and the gun is sufficiently powerful, eventually the point of landing is so far away that we must consider the curvature of the earth in finding where it lands.
In fact, the real situation is more dramatic—the earth’s curvature may mean the projectile never lands at all. This was envisioned by Newton in the Principia. The following diagram is from his later popularization, A Treatise of the System of the World , written in the 1680’s:
The mountaintop at V is supposed to be above the earth’s atmosphere, and for a suitable initial speed, the projectile orbits the earth in a circular path. In fact, the earth’s curvature is such that the surface falls away below a truly flat horizontal line by about five meters in 8,000 meters (five
p) What is the effective force of pulling on a wagon with a 53N force acting at 30^0 to the horizontal?
F
F sin : has to overcome weight
F cos just has to overcome friction
In this case the effective force along the horizontal is F cos = 53cos30 = 45.9 N
q) Find the effective force acting on the10 kg mass accelerating down the 30o^ ramp.
Its acceleration would be(no friction) = F = ma: 10a= 49; a = 4.9 m/s^2
2. Work and Energy
Work is the product of a force and displacement, but the displacement has to be in the same direction (and angle) as the force.
W = F*d
a)
35 o
A 22 N force is applied at an angle of 35o^ with the horizontal. How much work is done if a wagon is pulled for a distance of 12 m?
Horizontal component of force is Fcos = 22 cos35= 18.02 N W = Fd = 18.02 N(12m) =216 Nm = 216 J
b) If work is done to elevate a mass (raise it to a certain height), the energy as usual is not destroyed. The energy is stored as gravitational potential energy , Ep.
W= Fg*d
Ep = mgh
If a 10.0 kg mass is raised 3.0 m above the floor and rested on a shelf at that height, how much gravitational potential energy is gained?
Ep=10 kg(9.8 m/s^2 )(3) = 294 J
g) Total mechanical energy = potential energy+ kinetic energy.
Use this idea to find the kinetic and potential energy just before the toy car goes off the ramp. Also find its velocity in km/h just before it goes off the ramp.
4.0 kg at 3.0 m/s
3.0 m
At 10.0 m
Total mechanical energy = potential energy+ kinetic energy.
= mgh + 0.5mv^2 =4(9.8)(10) + 0.5(4)(3)^2. = 410 J
At 3.0 m,
Total mechanical energy = potential energy+ kinetic energy.
410 J = mgh + 0.5mv^2 410 J = 4(9.8)(3) + 0.5(4)v^2
v = 12 m/s
10 .0 m
Additional Problems for Mass, Force and Gravity
- If you go on a diet and lose weight, will you also lose mass? Explain.
- John weighed 980 N on Earth where gravity = 9.8 m/s^2. Before leaving for the moon, his wife cooked lots of pasta for him. When he reached the moon he weighed 167 N. How much mass did he gain from the pasta? Gravitational acceleration on the moon is 1.6 m/s^2.
- What force is required to accelerate a 3.0 kg mass by 2.0 /s^2?
- Which of the following graphs corresponds to the greatest mass? Explain.
A
B
C
- A loose leaf and a lead weight are dropped from the same height in a vacuum. Which, if any, hits the floor first?
- The different masses and radii of different planets account for different gravitational accelerations.
where mo = mass of the object on surface of planet gp = gravitational acceleration on planet G = gravitational constant mp = mass of planet rp = radius of planet a) Simplify the above formula to get a formula for g. What term cancels? b) Let gn = gravitational acceleration on planet Neptune. Write a similar expression for Earth’s gravity in terms of its radius re and mass me. c) Divide gn by ge to get a formula for how much stronger gravitational acceleration is on planet Neptune. What term cancels?
Force (N)
Acceleration (m/s^2 )
