12 kg wagon is being pulled at an angle of 38o above horizontal. What force is applied to the wagon if it accelerates from rest to a speed of 2.2 m/s over a distance of 3.4 m? Is this question a typo? Am I supposed to solve for force or work?

Physics - silverback, Tuesday, January 12, 2016 at 10:12pm
I need help
Physics - Damon, Tuesday, January 12, 2016 at 10:29pm
F cos 38 = m a

easy way is for constant acceleration
v average = (Vi+Vf)/2
so
v average = (0 + 2.2)/2 = 1.1 m/s
so time = t = 3.4/1.1 = 3.09 s
a = change in v / time
= 2.2 / 3.09
= .712 m/s^2
so
F cos 38 = 12 * .712

F = 10.8 Newtons
Physics - silverback, Tuesday, January 12, 2016 at 10:39pm
This is from one of your previous answers. You can do it with work if you wish or you can do it with F = m a

with work

work done = Force in direction of motion * distance
Force in direction of motion = F cos 38
= .788 F
work done = .788 F * 3.4 meters
= 2.68 F Joules

that is the increase in kinetic energy
(1/2) m v^2 = .5*12 * 2.2^2
= 29 Joules
so
2.68 F = 29
F = 10.8 Newtons
Why did you use kinetic energy is equal to work?

Conservation of energy

work done = increase of energy
or
work done = increase in kinetic energy + increase on potential energy

think lifting a barbell

work in = Force up * distance up
That is also the increase on potential energy m g h
when you drop it
that same value in Joules becomes (1/2) m v^2

Well, I guess we could say that work and kinetic energy are like peanut butter and jelly - they just go together! When an object is accelerated, work is done on it and that work ends up being equal to the change in its kinetic energy. It's like the kinetic energy is the trophy at the end of the race, and work is the sweat and tears that got you there. So, in this case, we used the equation for work to find the force applied to the wagon. Hope that clears things up!

In this problem, we can solve for the force using either the equation F = ma or by calculating the work done on the wagon.

Damon used the equation F = ma to calculate the force applied to the wagon. He first found the acceleration by dividing the change in velocity (2.2 m/s) by the time taken to achieve that change in velocity (3.09 s). Then, he multiplied the mass of the wagon (12 kg) by the acceleration to find the force.

On the other hand, Damon also mentioned that you can solve for the force using work. Work done is equal to the force in the direction of motion multiplied by the distance traveled. Since the wagon is pulled at an angle of 38 degrees above horizontal, the force in the direction of motion is given by F cos 38 degrees. Damon calculated this force and then multiplied it by the distance traveled (3.4 meters) to find the work done.

The reason Damon used the equation of kinetic energy being equal to work is because, in this problem, the work done on the wagon results in an increase in its kinetic energy. Thus, the work done can be set equal to the change in kinetic energy and the force can be solved for.

In this particular problem, the question asks for the force applied to the wagon as it accelerates. One way to calculate this force is by using Newton's second law: F = m * a, where F is the force, m is the mass, and a is the acceleration.

Another way to solve this problem is by using the concept of work. The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force applied is in the horizontal direction, and we can find it by using the component of the force in the direction of motion.

The component of the force in the direction of motion can be determined by taking the cosine of the angle between the force and the horizontal axis. In this case, the angle is 38 degrees, so the component of the force is F cos 38.

To find the work done, we multiply this force component by the distance over which the force is applied, which is 3.4 meters. Therefore, the work done is 0.788F * 3.4.

Since the work done on the wagon is equal to the increase in kinetic energy, we can equate the work done to the change in kinetic energy. The change in kinetic energy is given by (1/2) m v^2, where m is the mass of the wagon and v is its final velocity.

By equating the work done to the change in kinetic energy, we get the equation 0.788F * 3.4 = (1/2) * 12 * (2.2)^2.

Solving this equation will give us the force applied to the wagon, which is 10.8 Newtons.

Using kinetic energy in this problem is another approach to calculating the force, but Newton's second law is typically the more direct method.