Answer: The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Then the mass m is 0.625kg.
Explanation: To find the answer, we need to know more about the simple harmonic motion.
<h3>
What is simple harmonic motion?</h3>
- A particle is said to execute SHM, if it moves to and fro about the mean position under the action of restoring force.
- We have the equation of time period of a SHM as,
- Where, m is the mass of the body and k is the spring constant.
<h3>How to solve the problem?</h3>
- We have to find the value of m,
Thus, we can conclude that, the mass m will be 0.625kg.
Learn more about simple harmonic motion here:
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Answer:
Explanation:
3.4 m/s due North, -1.1 m/s due East
Answer:
3.735×10⁻⁶ N
Explanation:
From newton' s law of universal gravitation,
F = Gmm'/r² .............................. Equation 1
Where F = Gravitational force between the person and the refrigerator, m = mass of the person, m' = mass of the refrigerator, r = distance between the person and the refrigerator. G = gravitational universal constant.
Given: m = 70 kg, m' = 200 kg, r = 0.5 m
Constant: G = 6.67×10⁻¹¹ Nm²/kg².
F = (6.67×10⁻¹¹×70×200)/0.5²
F = 93380×10⁻¹¹/0.25
F = 373520×10⁻¹¹
F = 3.735×10⁻⁶ N
Hence the force between the person and the refrigerator = 3.735×10⁻⁶ N
Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of 
. As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:
notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:
When solving for r, we get:
so we can substitute this into our volume of a cone formula:
which simplifies to:
So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:
Which simplifies to:
So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:
Now we can substitute the provided values into our equation. So we get:
so:
