How Can a Man Move Cars Weighing 700 kN Using Only His Teeth?

[HappyDays]

Homework Statement

A man moves two passenger cars by clamping his teeth don a bit that was attached to the cars with a rope and then leaning backward while pressing his teeth against the railway ties. The car together weighed 700 kN. Assume that he pulled with a constant force which was 2.5 times his body weight, at an upward angle of 30 degrees from the horizontal. His mass was 80 kg, and he moved the cars 1.0m. Neglecting any retarding force from the wheel rotation, find the speed of the cars at the end of the pull.

d = 1.0m
theta = 30 degrees
force total = 2.5 x man's body weight
cars' weight = 700kN
man's mass = 80kg

Homework Equations

Just need help to get started. Thanks in advance.

The Attempt at a Solution

Don't understand how to find force only given distance and no time.

 

[ATeam232]

I am going to assume that since it is not mentioned, that this whole system is frictionless. Set up your coordinate system so that the origin is at the point of where the rope attaches to the cars. Do not tilt the coordinate system. Draw a free body diagram. You will have a normal force in the positive y direction and mg in the negative y direction. You will also have the force exerted on the cars (tension of the cable) by the man pulling with his teeth. You need to solve for the x and y components of this tension using trig. The hypotanuse of the right triangle will be the mass of the man times 2.5. All you really need is the force in the x direction since you are solving for velocity in the x direction. Once you have this force, you will be able to find the acceleration in the x direction using F=ma. Plug that into a 2D kinematics equation not involving time and you will have your velocity.

 

[Moetasim]

As a scientist, your first step would be to identify the relevant equations and principles that can help solve this problem. In this case, you can use Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). Additionally, you can also use the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy (W=ΔKE).

Next, you can break down the problem into smaller parts and apply these equations to each part. For example, you can first calculate the force exerted by the man by multiplying his body weight (80kg x 9.8m/s^2) by the given factor of 2.5. This will give you the total force applied to the cars.

Then, using the given distance (1.0m) and the angle (30 degrees), you can calculate the work done on the cars by the man using the formula W=Fdcosθ. This will give you the change in kinetic energy of the cars.

Finally, you can use the work-energy theorem to calculate the final velocity of the cars at the end of the pull. Since the problem states that there is no retarding force from wheel rotation, you can assume that all the work done by the man is converted into kinetic energy of the cars. Therefore, you can equate the work done by the man to the change in kinetic energy of the cars, and solve for the final velocity.

I hope this helps you get started on solving the problem. Remember to always identify the relevant equations and principles, break down the problem into smaller parts, and use units consistently throughout your calculations. Good luck!