Acceleration of a car

In summary, the conversation discusses how to determine the acceleration of a car based on the angle of a graduation tassel hanging from the rear-view mirror. The individual seeking help is unsure of where to start and which equations to use, but it is suggested to consider that acceleration is a vector and to use trigonometry to solve the problem.
  • #1
purcell2
2
0
1.
Your friend's 10.9-g graduation tassel hangs on a string from his rear-view mirror. When he accelerates from a stop light, the tassel deflects backward toward the rear of the car. If the tassel hangs at an angle of 5.60° relative to the vertical, what is the acceleration of the car?


I realize this isn't difficult. I think I'm making it more complicated than it needs to be because I'm not sure how to start/ which equations to use. There's acceleration in both directions so I need to set up the x and y components of the acceleration/force but beyond that I'm lost. Any help with setting it up/ and or solving it would be much appreciated! I would rather you show the steps to solve it than the answer if at all possible. Thank you so much!
 
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  • #2
Welcome to PF.

Consider that acceleration is a vector too.

If the tassel is being pulled radially, then you have a right triangle where g is the vertical, and a of car is the horizontal.

Consider then tan-1 of the sides?
 
  • #3


I would approach this problem by first identifying the given information and what is being asked. We are given the mass of the tassel (10.9 g) and the angle at which it deflects (5.60°). We are also given the fact that the car is accelerating from a stop light. Therefore, we need to determine the acceleration of the car.

To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). We can also use trigonometry to break down the acceleration into its x and y components.

Let's start by drawing a free-body diagram of the tassel hanging from the rear-view mirror. The only force acting on the tassel is its weight (mg), which can be broken down into its x and y components. The x component (F_x) will be equal to the tension in the string, and the y component (F_y) will be equal to the weight of the tassel (mg).

Next, we need to determine the acceleration of the car. Since the tassel is deflected backward, we know that the car is accelerating forward. We can represent this acceleration as a_x.

Using trigonometry, we can write the following equations:

F_x = ma_x
F_y = mg

We can also use the given angle to find the relationship between F_x and F_y:

tan(5.60°) = F_x/F_y

Solving for F_x, we get:

F_x = F_y * tan(5.60°)

Substituting this into our first equation, we get:

F_y * tan(5.60°) = ma_x

Since we know the mass of the tassel and the acceleration due to gravity (g), we can solve for F_y:

F_y = mg = 10.9 g * 9.8 m/s^2 = 106.82 g*m/s^2

Substituting this into our equation, we get:

106.82 g*m/s^2 * tan(5.60°) = ma_x

Simplifying, we get:

1.02 g*m/s^2 = ma_x

Finally, we can solve for the acceleration of the car (a_x):

a_x = (1.02 g*m/s^2)/m = 1.
 

What is acceleration?

Acceleration is the rate at which the velocity of an object changes over time. In other words, it measures how quickly an object's speed is increasing or decreasing.

How is acceleration calculated?

Acceleration can be calculated by dividing the change in an object's velocity by the time it takes for that change to occur. The formula for acceleration is a=Δv/Δt, where "a" represents acceleration, "Δv" represents the change in velocity, and "Δt" represents the change in time.

How does acceleration affect a car?

Acceleration is a crucial factor in how a car moves. When a car accelerates, it increases its speed, and when it decelerates, it decreases its speed. The acceleration of a car determines how quickly it can reach a certain speed, how fast it can stop, and how well it can navigate turns.

What factors affect the acceleration of a car?

Several factors can affect the acceleration of a car, including the car's engine power, weight, and aerodynamics. Other external factors such as friction, air resistance, and road conditions can also impact acceleration.

How can the acceleration of a car be improved?

The acceleration of a car can be improved by reducing the car's weight, increasing its engine power, and improving its aerodynamics. Regular maintenance and tuning can also help improve a car's acceleration by ensuring the engine is running at its best performance.

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