Answer:
The reading of the experiment made in air is 50 g more than the reading of the measurement made in water.
Explanation:
Knowing that the density of lead is 
and the volume, we can calculate the true weight of the piece of lead:
When the experiment is done in air, we can discard buoyancy force (due to different densities) made by air because it's negligible and the measured weight is approximately the same as the true weight.
When it is done in water, the effect of buoyancy force (force made by the displaced water) is no longer negligible, so we have to take it into account.
Knowing that the density of water is 1 g per cubic centimeter, and that the volume displaced is equal to the piece of lead (because of its much higher density, the piece of lead sinks), we can know that the buoyancy force made by water is 50 g, opposite to the weight of the lead.
Now that we have the two measurements, we can calculate the difference:
The reading of the experiment made in air is 50 g more than the reading of the measurement made in water.
Answer:
D) 42.87 m/s
Explanation:
First, find the time it takes him to land. Given in the y direction:
Δy = 60 m
v₀ = 0 m/s
a = 9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
60 m = (0 m/s) t + ½ (9.8 m/s²) t²
t = 3.5 s
Next, find the speed needed to travel the horizontal distance in that time. Given in the x direction:
Δx = 60 m
a = 0 m/s²
t = 3.5 s
Find: v₀
Δy = v₀ t + ½ at²
150 m = v₀ (3.5 s) + ½ (0 m/s²) (3.5 s)²
v₀ = 42.87 m/s
Answer:
1.024 × 10⁸ m
Explanation:
The velocity v₀ of the orbit 8RE is v₀ = 8REω where ω = angular speed.
So, ω = v₀/8RE
For the orbit with radius R for it to maintain a circular orbit and velocity 2v₀, we have
2v₀ = Rω
substituting ω = v₀/8RE into the equation, we have
2v₀ = v₀R/8RE
dividing both sides by v₀, we have
2v₀/v₀ = R/8RE
2 = R/8RE
So, R = 2 × 8RE
R = 16RE
substituting RE = 6.4 × 10⁶ m
R = 16RE
= 16 × 6.4 × 10⁶ m
= 102.4 × 10⁶ m
= 1.024 × 10⁸ m
Answer:
Explanation:
From Newton's second law,
where 
is the force, 
is the mass and 
is the acceleration.
From Hooke's law,
where 
is the spring constant and 
is the displacement function measured from the origin. The negative sign indicates the force acts in opposite direction to the displacement. In fact, it is a restoring force; it acts to return the spring to its original undisturbed position.
Since both forces are the same,
The implication of this is that the acceleration is proportional to the displacement but opposite to it. That last statement is the definition of a simple harmonic motion which this is.
The ratio 
is a constant except in situations where the mass is varying (say, the mass on the spring is a decaying material).
Answer:
n (a neutron)
Explanation:
For a chemical element:
- The lower subscript indicates the atomic number (the number of protons)
- The upper subscript indicates the mass number (the sum of protons and neutrons in the nucleus)
In the reaction described in the problem, we see that a gamma photon hits a nucleus of Calcium-40, which has
Z = 20 (20 protons)
A = 40 (40 protons+neutrons)
Which means that the number of neutrons is n = A - Z = 40 - 20 = 20
After the reaction, we have a nucleus of Calcium-39, which has
Z = 20 (20 protons)
A = 39 (39 protons+neutrons)
Which means that the number of neutrons is n = A - Z = 40 - 39 = 19
So, the nucleus has lost 1 neutron, which is the particle missing in the reaction.
