A dynamics cart with a friction pad is placed at the top of an inclined track and released fromrest. The cart accelerates down the incline at a rate of 0.60 m/s2. If the track is angled at 10degrees above the horizontal, determine the coefficient of kinetic friction between the cart andthe track.
Answers
Answer:
0.114
Explanation:
There are two forces acting on the cart in the direction along the cart:
- The component of the gravitational force in the direction parallel to the ramp, , down along the ramp
- The force of friction, , up along the ramp
So the equation of motion along this direction is:
(1)
where
m is the mass of the cart
is the acceleration due to gravity
is the angle of the ramp
is the coefficient of kinetic friction
N is the normal force exerted by the ramp on the cart
is the acceleration of the cart
The normal force can be found from the equation of the forces along the direction perpendicular to the ramp; in fact, the normal force is balanced by the component of the weight perpendicular to the ramp, so we have:
From which we get:
Substituting into (1),
And solving for , we find the coefficient of friction:
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Define the term energy density of a body under strain
The height h (in feet) of an object shot into the air from a tall building is given by the function h(t) = 650 + 80t − 16t2, where t is the time elapsed in seconds. (a) Write a formula for the velocity of the object as a function of time t.
A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is 9.70 MHz . At this field strength, the Hall voltage on the probe is 0.549 mV when the current through the probe is 0.146 mA . Later, when an unknown magnetic field is measured, the Hall voltage at the same current is 1.735 mV .A) What is the strength of this magnetic field?
A. 5.7 m/s
B. 2.6 m/s
C. 13.9 m/s
D. 7.2 m/s
SUBMIT
Answers
Answer:
D
Explanation:
0.3=v-6/4
make v the subject
v=7.2ms^2
Answers
What is pseudo force?
A pseudo force, also called a fictitious force or an inertial force, is an apparent force that acts on all bodies whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.
Answers
a. There are two main types of pluralism: cultural and political
b. Yes, the United States is becoming more pluralistic
c. Ethnic enclaves can be both a positive and negative aspect of pluralism in the US.
a. Pluralism refers to the coexistence of multiple cultures, religions, and ethnicities within a society. There are two main types of pluralism: cultural and political. Cultural pluralism emphasizes the preservation of distinct cultural traditions, while political pluralism emphasizes the equal representation of different groups within the political system.
Cultural pluralism is often associated with the idea of multiculturalism, which recognizes and celebrates the diversity of different cultures. This type of pluralism acknowledges the importance of cultural differences and encourages individuals to maintain and express their cultural identities. In contrast, political pluralism emphasizes the importance of equal representation of different groups within the political system. This can take the form of proportional representation in government or equal access to political power for different groups.
b. The United States is becoming more pluralistic, as the population becomes more diverse and the importance of multiculturalism and political pluralism is increasingly recognized. The country is home to many different ethnic and cultural groups, and these groups are increasingly visible in politics and society. This is evident in the increasing number of ethnic and cultural enclaves, which are areas where different ethnic groups live in close proximity to one another.
c. Ethnic enclaves can be both a positive and negative aspect of pluralism in the US. On the one hand, they allow individuals to maintain their cultural traditions and create supportive communities. On the other hand, they can also lead to segregation and exclusion, as different groups may be reluctant to interact with one another. In order to promote a positive form of pluralism, it is important to encourage interaction and understanding between different groups, while also respecting and celebrating their distinct cultural identities.
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b. tension and gravity
c. tension, gravity, and the centripetal force
d. tension, gravity, the centripetal force, and friction
Answers
Final answer:
The forces directly acting on the ball hanging from a rear-view mirror while a car drives in a circle are tension, gravity, and the centripetal force.
Explanation:
The correct answer is c. tension, gravity, and the centripetal force.
When the car is driving in a circle, the ball experiences both tension and gravity. The tension in the string is what keeps the ball from falling, while gravity pulls the ball downward.
In addition to tension and gravity, the ball also experiences the centripetal force. This force is directed towards the center of the circular motion and keeps the ball moving in a circular path.
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Answers
Answer:
The add mass = 5.465 kg
Explanation:
Note: Since the spring is the same, the length and Tension are constant.
f ∝ √(1/m)........................ Equation 1 (length and Tension are constant.)
Where f = frequency, m = mass of the spring.
But f = 1/T ..................... Equation 2
Substituting Equation 2 into equation 1.
1/T ∝ √(1/m)
Therefore,
T ∝ √(m)
Therefore,
T₁/√m₁ = k
where k = Constant of proportionality.
T₁/√m₁ = T₂/√m₂ ........................ Equation 3
making m₂ the subject of the equation
m₂ = T₂²(m₁)/T₁²........................... Equation 4
Where T₁ = initial, m₁ = initial mass, T₂ = final period, m₂ = final mass.
Given: T₁ = 1.18 s m₁ = 0.50 kg, T₂ = 2.07 s.
Substituting into equation 4
m₂ = (2.07)²(0.5)/(1.18)²
m₂ = 4.285(1.392)
m₂ = 5.965 kg.
Added mass = m₂ - m₁
Added mass = 5.965 - 0.5
Added mass = 5.465 kg.
Thus the add mass = 5.465 kg
Answers
(a) It takes approximately 2.8956 seconds for the camera to reach the ground.
(b) The velocity of the camera just before it lands is approximately -28.375 m/s (downward).
We have,
Given information:
Initialheight (h₀) = 41 m (above the ground)
Descentrate of the hot-air balloon = -2.3 m/s (negative because it's descending)
We can use the kinematicequations to solve for the time it takes for the camera to reach the ground and its velocity just before landing.
(a)
To find the time it takes for the camera to reach the ground, we can use the following kinematic equation:
h = h₀ + (v₀)t + (1/2)at²
Where:
h = final height (0 m, as it reaches the ground)
h₀ = initial height (41 m)
v₀ = initial velocity (0 m/s, as the camera is dropped)
a = acceleration (acceleration due to gravity, approximately -9.8 m/s²)
t = time (what we're solving for)
Plugging in the values:
0 = 41 + (0)t + (1/2)(-9.8)t²
Simplifying:
-4.9t² = 41
Divide by -4.9:
t² = -41 / -4.9
t² = 8.36734694
Taking the square root:
t = √8.36734694
t ≈ 2.8956 seconds
(b)
To find the velocity just before the camera lands, we can use the following kinematic equation:
v = v₀ + at
Where:
v = final velocity (what we're solving for)
v₀ = initial velocity (0 m/s)
a = acceleration (acceleration due to gravity, -9.8 m/s²)
t = time (2.8956 seconds, calculated in part a)
Plugging in the values:
v = 0 + (-9.8)(2.8956)
v ≈ -28.375 m/s
The negativesign indicates that the velocity is directed downward, which is consistent with the descending motion.
Thus,
(a) It takes approximately 2.8956 seconds for the camera to reach the ground.
(b) The velocity of the camera just before it lands is approximately -28.375 m/s (downward).
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