4. When setting goals, you should do everything EXCEPT which of the following?
1 answer:
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Refer to the diagram shown below.
The basket is represented by a weightless rigid beam of length 0.78 m.
The x-coordinate is measured from the left end of the basket.
The mass at x=0 is 2*0.55 = 1.1 kg.
The weight acting at x = 0 is W₁ = 1.1*9.8 = 10.78 N
The mass near the right end is 1.8 kg.
Its weight is W₂ = 1.8*9.8 = 17.64 N
The fulcrum is in the middle of the basket, therefore its location is
x = 0.78/2 = 0.39 m.
For equilibrium, the sum of moments about the fulcrum is zero.
Therefore
(10.78 N)*(0.39 m) - (17.64 N)*(x-0.39 m) = 0
4.2042 - 17.64x + 6.8796 = 0
-17.64x = -11.0838
x = 0.6283 m
Answer: 0.63 m from the left end.
The basket is represented by a weightless rigid beam of length 0.78 m.
The x-coordinate is measured from the left end of the basket.
The mass at x=0 is 2*0.55 = 1.1 kg.
The weight acting at x = 0 is W₁ = 1.1*9.8 = 10.78 N
The mass near the right end is 1.8 kg.
Its weight is W₂ = 1.8*9.8 = 17.64 N
The fulcrum is in the middle of the basket, therefore its location is
x = 0.78/2 = 0.39 m.
For equilibrium, the sum of moments about the fulcrum is zero.
Therefore
(10.78 N)*(0.39 m) - (17.64 N)*(x-0.39 m) = 0
4.2042 - 17.64x + 6.8796 = 0
-17.64x = -11.0838
x = 0.6283 m
Answer: 0.63 m from the left end.
a. The free-body diagram for the glass when it is at the top of the circle is attached below.
b. The equation for the net force on the glass at the top of the circle in terms of w, Fn, m, v, and r is mg x g + N - mg x Vtop² /R =0
c. The glass will fall out of the bucket if the normal force between the glass and bucket equals zero. The speed with which she spin the bucket to prevent this from happening is 3.83 m/s.
d. The string will break if the tension on it is more than 100 N. The range of speeds can prevent the string from breaking is 3.83< Vtop<4.99 m/s
<h3>What is Net force?</h3>When two or more forces are acting on the system of objects, then the to attain equilibrium, net force must be zero.
Given, Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket. She spins the bucket in a vertical circle of radius 1.5 m. She must swing the bucket to keep the glass from falling out.
a. The free body diagram of the bucket and glass is attached below.
b. Bucket will undergo centrifugal force
Fb = mVtop² /R
From the equilibrium of forces, we have
For bucket,
T +mb xg - N = mb x Vtop² /R..............(1)
For glass,
mg x g + N = mg x Vtop² /R..............(2)
Thus, this is the net force equation on the glass.
c. On adding both the equations. we have
T + (mb + mg) xg = (mb + mg) Vtop² /R
Substituting the values, T = 0 and from the question, we get
0 + (2+0.5) 9.81 = (2+0.5)(Vtop²/0.5)
Vtop = 3.83 m/s
Thus, the speed of spin to prevent glass from falling out is 3.83 m/s
d. The string will break if the tension on it is more than 100 N
100 + (2+0.5) 9.81 = (2+0.5)(Vtop²/0.5)
Vtop = 4.99 m/s
Thus, the range of velocity is 3.83< Vtop<4.99 m/s
Learn more about net force.
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1) C. velocity
Acceleration is defined as the rate of change of velocity per unit time. In formulas:
where
is the change in velocity
is the time interval
Therefore, the correct answer is C. velocity.
2) A. 9.8m/s/s
Earth's gravity is a force, so it produces an acceleration on every object with mass located on the Earth's surface. This acceleration can be calculated, as it is given by the formula
where
is the gravitational constant
is the Earth's mass
is the Earth's radius
By substituting these numbers into the formula, one can find that the acceleration due to Earth's gravity is .