Magnitude of the force

In summary, a car with a weight of 1.5×104 N is stopped from a speed of 45 km/h to 0 m/s in a distance of 12m. Using the equation for final velocity, it was determined that the mass of the car is 1.53e3 kg. The method used to find the acceleration was correct, but the equation used to find the force, F=ma, may not be applicable. Instead, the equation F = mv^2/2d, which uses energy, may be more direct in finding the magnitude of the force.
  • #1
bearhug
79
0
A car that weighs 1.5×104 N is initially moving at a speed of 45 km/h when the brakes are applied and the car is brought to a stop in 12 m. Assuming that the force that stops the car is constant, find the magnitude of that force.

I found the mass to be 1.53e3 kg then I figured now I need to find the acceleration using the information that I have so I used the equation
Vf^2 = Vi^2 + 2a(Xf-Xi)
Vi = 12.5 m/s
Vf = 0 m/s
Xf = 12m
Xi= 0 m

Then plug the acceleration value into the equation F= ma but apparently that's wrong. Is this the correct method?
 
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  • #2
bearhug said:
A car that weighs 1.5×104 N is initially moving at a speed of 45 km/h when the brakes are applied and the car is brought to a stop in 12 m. Assuming that the force that stops the car is constant, find the magnitude of that force.

I found the mass to be 1.53e3 kg then I figured now I need to find the acceleration using the information that I have so I used the equation
Vf^2 = Vi^2 + 2a(Xf-Xi)
Vi = 12.5 m/s
Vf = 0 m/s
Xf = 12m
Xi= 0 m

Then plug the acceleration value into the equation F= ma but apparently that's wrong. Is this the correct method?
Method is ok. [itex]a = \Delta v/\Delta t \text{ where } \Delta t = 2d/v_i[/itex] Since final velocity is 0, you have: a = v^2/2d

You are in effect using energy: [itex]KE = F*d = \frac{1}{2}mv^2[/tex] which is a little more direct:

[tex]F = mv^2/2d[/tex]

AM
 
  • #3


I would like to commend you on your approach to solving this problem. It appears that you have correctly identified the initial velocity, final velocity, and displacement of the car, and have used the appropriate equations to solve for acceleration. However, I believe the issue lies in your calculation for mass. The weight of the car, given in the problem as 1.5×104 N, is not the same as its mass. To find the mass, you would need to divide the weight by the acceleration due to gravity (9.8 m/s^2). This would give you a mass of approximately 1530 kg.

Once you have the correct mass value, you can then use the equation F=ma to calculate the magnitude of the force that stops the car. This force would be equal to the mass (1530 kg) multiplied by the acceleration (which you have correctly calculated as -4.17 m/s^2). This gives a magnitude of force of approximately 6381 N.

I hope this helps clarify the process for finding the magnitude of the force in this scenario. Keep up the good work in applying scientific principles to solve problems!
 

What is the magnitude of force?

The magnitude of force is the measurement of the strength or intensity of a force. It is typically measured in units of newtons (N) in the metric system or pounds (lbs) in the imperial system.

How is the magnitude of force calculated?

The magnitude of force is calculated by multiplying the mass of an object by its acceleration. This is represented by the equation F=ma, where F is force, m is mass, and a is acceleration. The resulting unit of force will depend on the units used for mass and acceleration.

Is the magnitude of force the same as the direction of force?

No, the magnitude of force and the direction of force are two separate components of a force vector. The magnitude refers to the strength or intensity of the force, while the direction refers to the path or angle in which the force is applied.

What factors can affect the magnitude of force?

The magnitude of force can be affected by several factors including the mass of an object, the speed or velocity of an object, the angle or direction of the force, and the presence of other forces acting on the object.

How does the magnitude of force relate to motion?

The magnitude of force is directly proportional to the acceleration of an object. This means that the greater the magnitude of force, the greater the acceleration of an object. In other words, a larger force will cause an object to move faster or change direction more quickly.

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