Now that you have a broader understanding of some basic concepts from the world of Physics, create a new hypothetical experiment from your own life experience that helps explain one of the concepts. Think in simple terms, and explain what you expect your experiment to uncover. For your response, provide an alternative experiment to your classmates’ post.
Tag: Physics
Physics
Question 1 (6 marks)
a) Newton’s universal law of gravitation describes the force of gravity acting on two masses. The
correct equation is,
Fg = G
m1m2
r
2
.
Using dimensional analysis, determine the dimensions and SI units for the gravitational constant
G. Here, Fg is a force, m1 and m2 are masses and r is a distance. (2 marks)
b) Someone then tells you that the equation for gravitational potential energy U (measured in
Joules) is,
U = −G
m1m2
r
3
.
Using dimensional analysis, determine if they are correct. (1 mark)
c) An experiment determined that the time for a star to orbit a black hole T in a circular orbit
depends on the distance from the black hole to the star r, the gravitational constant G and the
mass of the black hole m. That is,
T = CrαG
βmγ
where C is a dimensionless constant. Using only dimensional analysis, determine what the
exponents α, β and γ must be for this equation to be correct. (3 marks)
Question 2 (7 marks)
Answer the following given the two vectors written in standard position.
A⃗ = 4m/s @ 220o B⃗ = 7m/s @ 300o
a) Draw a diagram for A⃗ and write A⃗ in terms of ˆi and ˆj (answer to 2 decimal places). (2 marks)
b) Draw a diagram for B⃗ and write B⃗ in terms of ˆi and ˆj (answer to 2 decimal places). (2 marks)
c) Determine the angle θ between A⃗ and B⃗ using the dot product. Then draw a diagram and use
geometry to verify your answer. (3 marks)
Question 3 (8 marks)
Answer the following given the two vectors (measured in meters).
A⃗ = −4ˆi + 10ˆj + ˆk B⃗ = 5ˆi + 5ˆk
a) Using only the dot product (no cross products) determine a unit vector Cˆ that is perpendicular
to both A⃗ and B⃗ . I recommend checking that your answer is indeed perpendicular to both A⃗ and
B⃗ by taking a dot product with each. (6 marks)
b) Determine the angle ϕ (Greek letter for F, pronounced ’f-eye’) between Cˆ and the z-axis (answer
to 2 decimal places). (2 marks)
Physics
Question 1 (6 marks)
a) Newton’s universal law of gravitation describes the force of gravity acting on two masses. The
correct equation is,
Fg = G
m1m2
r
2
.
Using dimensional analysis, determine the dimensions and SI units for the gravitational constant
G. Here, Fg is a force, m1 and m2 are masses and r is a distance. (2 marks)
b) Someone then tells you that the equation for gravitational potential energy U (measured in
Joules) is,
U = −G
m1m2
r
3
.
Using dimensional analysis, determine if they are correct. (1 mark)
c) An experiment determined that the time for a star to orbit a black hole T in a circular orbit
depends on the distance from the black hole to the star r, the gravitational constant G and the
mass of the black hole m. That is,
T = CrαG
βmγ
where C is a dimensionless constant. Using only dimensional analysis, determine what the
exponents α, β and γ must be for this equation to be correct. (3 marks)
Question 2 (7 marks)
Answer the following given the two vectors written in standard position.
A⃗ = 4m/s @ 220o B⃗ = 7m/s @ 300o
a) Draw a diagram for A⃗ and write A⃗ in terms of ˆi and ˆj (answer to 2 decimal places). (2 marks)
b) Draw a diagram for B⃗ and write B⃗ in terms of ˆi and ˆj (answer to 2 decimal places). (2 marks)
c) Determine the angle θ between A⃗ and B⃗ using the dot product. Then draw a diagram and use
geometry to verify your answer. (3 marks)
Question 3 (8 marks)
Answer the following given the two vectors (measured in meters).
A⃗ = −4ˆi + 10ˆj + ˆk B⃗ = 5ˆi + 5ˆk
a) Using only the dot product (no cross products) determine a unit vector Cˆ that is perpendicular
to both A⃗ and B⃗ . I recommend checking that your answer is indeed perpendicular to both A⃗ and
B⃗ by taking a dot product with each. (6 marks)
b) Determine the angle ϕ (Greek letter for F, pronounced ’f-eye’) between Cˆ and the z-axis (answer
to 2 decimal places). (2 marks)