Solving Physics Problems: Problem 3 & 5

In summary, Problem 3 involves a dog sitting 1.4 m from the center of a merry-go-round and undergoing a 1.7 m/s^2 centripetal acceleration. The question is asking for the angular speed of the merry-go-round in units of rad/s. Problem 5 involves a girl sitting on a tire attached to an overhanging tree limb by a rope 2.30 m in length. She is pushed by her father with a tangential speed of 3.05 m/s. The force maintaining her circular motion is 84.7 N, not including the force opposing her weight. The question is asking for the girl's mass in units of kg.
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Problem 3.
A dog sits 1.4 m from the center of a merry-go-round. The dog undergoes a 1.7 m/s^2 centripetal acceleration. What is the angular speed of the merry-go-round? Answer in units of rad/s.

Problem 5.
A girl sits on a tire that is attached to an overhanging tree limb by a rope 2.30 m in length. The girl's father pushes her with a tangential speed of 3.05 m/s. Besides the force opposing the girl's weight, the magnitude of the force that maintains her circular motion is 84.7 N.
What is the girl's mass? Answer in units of kg.
Note: How would you solve this?
 
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For Problem 3, we can use the formula for centripetal acceleration, a = ω^2r, where ω is the angular speed and r is the distance from the center. Plugging in the given values, we get ω = √(a/r) = √(1.7 m/s^2 / 1.4 m) = 1.15 rad/s.

For Problem 5, we can use the formula for tangential acceleration, a = αr, where α is the angular acceleration and r is the distance from the center. We can also use the formula for centripetal force, F = mv^2/r, where m is the mass and v is the tangential speed. Since the force opposing the girl's weight is not mentioned, we can assume that it is negligible and only consider the centripetal force. Setting these two formulas equal to each other, we get αr = mv^2/r. Rearranging, we get m = αr^2/v^2. Plugging in the given values, we get m = (84.7 N * 2.30 m) / (3.05 m/s)^2 = 12.7 kg. This is the mass of the girl.
 

What is the best approach to solving Physics Problem 3?

The best approach to solving Physics Problem 3 is to carefully read and understand the question, identify the relevant equations and variables, and then systematically work through the problem using those equations. It may also be helpful to draw diagrams or make a list of known and unknown quantities.

How can I check my answer for Physics Problem 3?

To check your answer for Physics Problem 3, you can plug your calculated values back into the original equation and see if it results in the same value as given in the problem. You can also use units to check for accuracy and make sure they match the expected units for the answer.

What is the most common mistake made when solving Physics Problem 5?

The most common mistake made when solving Physics Problem 5 is forgetting to convert units. It is important to pay attention to units and make sure they are consistent throughout the problem, especially when using equations that involve different units.

How can I improve my problem-solving skills for Physics?

To improve your problem-solving skills for Physics, it is important to practice regularly by attempting different types of problems and working through them step by step. It can also be helpful to work with a study group or seek out additional resources, such as textbooks or online tutorials.

What should I do if I am stuck on a Physics problem?

If you are stuck on a Physics problem, it can be helpful to take a break and come back to it later with a fresh perspective. You can also try approaching the problem from a different angle or seeking help from a classmate, teacher, or tutor. It is important to not get discouraged and keep practicing and learning from mistakes.

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