Solving for Acceleration: 8.3kg Block & 25.3° Angle

In summary, a block of mass 8.3 kg is being pulled by a cord with a force of 53.0 N at a 25.3° angle above the horizontal on a frictionless floor. To find the acceleration of the block, you can separate the applied force into its horizontal and vertical components using trigonometric ratios or the method of tension coefficients. An equation can then be set up, with the horizontal and vertical components equal to the mass times the acceleration.
  • #1
chaotixmonjuish
287
0
A block of mass 8.3 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of 53.0 N at an angle 25.3° above the horizontal. What is the magnitude of the acceleration of the block?

I'm just wondering how I set up an equation with an angle.
 
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  • #2
Separate the applied force into its horizontal and vertical components using the trigonometric ratios or use the method of tension co-efficients.
 
  • #3
That's where I'm having a problem.

would it be something like:

y=(mass)(sin(30)a)
x=(mass)(cos(30)a)
 
  • #4
How about [tex]F_x = F(cos (\frac{\pi}{6})) [/tex] ?
 
  • #5
wow, how did you get that
 
  • #6
chaotixmonjuish said:
That's where I'm having a problem.

would it be something like:

y=(mass)(sin(30)a)
x=(mass)(cos(30)a)
Yes, something like that. But of course the angle isn't 30 degrees.
 

1. How do you calculate acceleration in this scenario?

To calculate acceleration in this scenario, we will use the formula acceleration = (net force)/(mass). In this case, we have a mass of 8.3kg and an applied force at a 25.3° angle. We will need to find the component of the force that is acting parallel to the direction of motion in order to calculate the net force. Once we have the net force, we can plug it into the formula to find the acceleration.

2. Can you provide an example of solving for acceleration in this situation?

Sure, let's say we have a block with a mass of 8.3kg and an applied force of 100N at a 25.3° angle. We can use trigonometry to find the component of the force parallel to the direction of motion. In this case, the component would be 100N * cos(25.3°) = 90.6N. This is our net force. Plugging it into the formula acceleration = (90.6N)/(8.3kg), we get an acceleration of 10.9 m/s².

3. What are the units of acceleration in this scenario?

The units of acceleration in this scenario would be meters per second squared (m/s²). This is a unit of acceleration commonly used in physics to measure the change in velocity over time.

4. How is acceleration related to the motion of the block?

Acceleration is directly related to the motion of the block. It describes the rate at which the velocity of the block is changing. If the acceleration is positive, the block is speeding up. If the acceleration is negative, the block is slowing down. If the acceleration is zero, the block is moving at a constant velocity.

5. Can you explain how the angle of the applied force affects the acceleration of the block?

Yes, the angle of the applied force can affect the acceleration of the block. If the force is applied at a 0° angle (parallel to the direction of motion), it will contribute to the acceleration of the block. However, if the force is applied at a 90° angle (perpendicular to the direction of motion), it will not contribute to the acceleration. The component of the force that is parallel to the direction of motion is the only part that affects acceleration.

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