Kinetics, force and acceleration

In summary: After summing up the vertical components, I got N = 755.2 N and a = 1.75 m/s2.In summary, the crate with a mass of 80 kg is towed at an angle of 20º from the horizontal with a coefficient of static friction of μs = 0.4, a coefficient of kinetic friction of μk = 0.3, and a towing force of P = (90t2) N. By considering the vertical components of the forces, the crate's acceleration at t = 2 s is determined to be 1.75 m/s2, which is higher than the value of 1.46 m/s2 calculated without taking into account the vertical forces
  • #1
red123
22
0

Homework Statement



The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20º from the horizontal has shown. Determine the crate's acceleration in t = 2 s if the coefficient of static friction is μs = 0.4, the coefficient of kinetic friction is μk = 0.3, and the towing force is P = (90t2) N, where t is in seconds.

rau7pi.jpg


Homework Equations



ΣF = ma

The Attempt at a Solution



ΣFx = max
Pcos(20º) - μkmg = ma
84.57t2 - 235.44 = (80 kg)a

solving for a when t = 2
a = 1.29 m/s2

The answer at the back of my book is a = 1.75 m/s2. I think I'm supposed to consider that static friction force is greater than kinetic friction force, but I can't figure out how to do that.
 
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  • #2
red123 said:
ΣFx = max
Pcos(20º) - μkmg = ma
The force of friction is μN, but N does not simply equal mg. Solve for N, taking into consideration that the applied force is at an angle.
 
  • #3
Doc Al said:
The force of friction is μN, but N does not simply equal mg. Solve for N, taking into consideration that the applied force is at an angle.

Then N = mg*cos(20°)?
But that gives a = 1.46 m/s2, not a = 1.75 m/s2.
 
  • #4
red123 said:
Then N = mg*cos(20°)?
How did you come to that conclusion?

To solve for N, add up the vertical components of all forces acting on the body. (N is one of those forces.) The sum must be zero, since the body is not accelerating vertically.
 
  • #5
Thank you, Doc Al.
 

1. What is kinetics?

Kinetics is the branch of physics that studies the motion of objects and the forces that cause them to move.

2. What is force?

Force is a push or pull that causes an object to accelerate or change its motion.

3. How is acceleration calculated?

Acceleration is calculated by dividing the change in velocity by the change in time. The formula is a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

4. What is the relationship between force and acceleration?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on the object, and inversely proportional to the mass of the object. This means that the greater the force acting on an object, the greater its acceleration will be.

5. How do kinetic energy and potential energy relate to acceleration?

Kinetic energy and potential energy are both forms of energy that an object possesses due to its motion or position. The relationship between them and acceleration is described by the Work-Energy Theorem, which states that the net work done on an object is equal to the change in its kinetic energy. This means that if an object is accelerating, its kinetic energy is changing, either increasing or decreasing.

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