1 dimentional kinematics problem. due in 5 hours

In summary, the bolt came loose from an elevator moving upward at a speed of 7.1 m/s and reached the bottom of the elevator shaft in 3.6 s. To find the height of the elevator, the equation v=x/t can be used. To find the speed of the bolt when it hits the bottom of the shaft, the equation a=v/t can be used with a being the acceleration due to gravity. When dealing with constant velocity, the acceleration is zero and simpler equations can be used.
  • #1
the guy
1
0

Homework Statement


A bolt comes loose from underneath an elevator that is moving upward at a speed of 7.1 m/s. The bolt reaches the bottom of the elevator shaft in 3.6 s.
(a) How high up was the elevator when the bolt came loose?


(b) What is the speed of the bolt when it hits the bottom of the shaft?


Homework Equations


v=v0+ at
(x-x0)=vot+.5at^2
V^2=V0^2 -2a(x-x0)


The Attempt at a Solution



Im confused as if the acceleration of the elevator is constant or not, i can't seem to find it
 
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  • #2
The elevator is not accelerating, it only has a velocity.
You can find the height of the elevator using the equation for velocity: v=x/t.
You are trying to find x; you have t and v.
What do you have to do to find x?

To find the speed of the bolt when it hits the ground, remember that a=v/t. You are trying to find v (the speed), and you have t. You also have a, which is the acceleration due to gravity, 9.8 m/s2. You just need to do simple algebra for both of these problems.

Oh, by the way, remember that if something just has a velocity, its acceleration is zero. The equations you have listed are more complicated than this problem requires, but when you need them later, something moving with constant velocity has zero acceleration. So you might just need the x0 + v0t parts of the equation, for example.
 
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  • #3
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I would approach this problem by first identifying the known and unknown variables. The known variables in this problem are the elevator's initial speed (v0 = 7.1 m/s), the time it takes for the bolt to reach the bottom of the shaft (t = 3.6 s), and the acceleration due to gravity (a = 9.8 m/s^2). The unknown variables are the height of the elevator when the bolt comes loose and the speed of the bolt when it hits the bottom of the shaft.

Next, I would use the equations for 1-dimensional kinematics to solve for the unknown variables. Since the elevator is moving upward at a constant speed, the acceleration is zero (a = 0). Therefore, we can use the equation v = v0 + at to find the final velocity of the bolt when it reaches the bottom of the shaft. Plugging in the known values, we get v = 7.1 + 0(3.6) = 7.1 m/s.

To find the height of the elevator when the bolt came loose, we can use the equation (x - x0) = v0t + 0.5at^2. Since we want to find the initial height of the elevator (x0), we can rearrange the equation to solve for x0. Plugging in the known values, we get x0 = 0 + 0.5(9.8)(3.6)^2 = 63.9 m.

Therefore, the elevator was 63.9 m above the bottom of the shaft when the bolt came loose. And the speed of the bolt when it hits the bottom of the shaft is 7.1 m/s.
 

1. What is 1-dimensional kinematics?

1-dimensional kinematics is the study of motion in a straight line. It involves analyzing the position, velocity, and acceleration of an object as it moves along a single axis.

2. What are the key equations used in 1-dimensional kinematics?

The key equations used in 1-dimensional kinematics are the equations of motion:
- Position (x) = initial position (x0) + initial velocity (v0)t + 0.5(acceleration)(time squared)2
- Velocity (v) = initial velocity (v0) + (acceleration)(time)
- Acceleration (a) = (final velocity - initial velocity)/time

3. How do you solve a 1-dimensional kinematics problem?

To solve a 1-dimensional kinematics problem, you need to first identify the known values and the unknown value. Then, use the appropriate equation(s) to calculate the unknown value. It is important to pay attention to units and to use the correct sign (+ or -) for velocity and acceleration.

4. What is the difference between velocity and speed in 1-dimensional kinematics?

In 1-dimensional kinematics, velocity is a vector quantity that includes both magnitude (speed) and direction, while speed is a scalar quantity that only represents the magnitude of an object's motion. This means that velocity can be positive or negative depending on the direction of motion, while speed is always positive.

5. How does acceleration affect an object's motion in 1-dimensional kinematics?

Acceleration is the rate of change of an object's velocity over time. In 1-dimensional kinematics, if an object has a constant acceleration, it will either increase or decrease its velocity at a constant rate. If the acceleration is positive, the object will speed up, and if the acceleration is negative, the object will slow down. If the acceleration is zero, the object will either remain at a constant velocity or be at rest.

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