Can someone post numerical answers!!
Under less than ideal conditions, a student pushes a 6 kg cart holding 2 boxes of books up a ramp to a platform that is 1.8 m high in 42 sec. Each box contains 12 kg of books. The ramp is inclined at an angle of 15 degrees. He pushes w/ a steady force of 70 N to move it up.
Find: -Work in
-Work out
-IMA
-AMA
-Efficiency
-Power
What part of show your work/thinking do you not understand?
To find the answers to these questions, we'll need to use several formulas related to work, mechanical advantage, efficiency, and power. Let's break down each question one by one.
Work In:
The work done on an object can be calculated using the formula: work = force * distance * cos(theta), where force is the applied force, distance is the displacement, and theta is the angle between the applied force and the displacement. In this case, the applied force is 70 N, and the displacement can be calculated using the height and the angle of the ramp.
Step 1: Calculate the displacement using the height and the angle of the ramp.
Displacement = height / sin(theta)
Displacement = 1.8 m / sin(15 degrees)
Step 2: Calculate the work in.
Work In = force * displacement * cos(theta)
Work In = 70 N * displacement * cos(15 degrees)
Work Out:
The work done on an object can also be calculated by multiplying the force applied in the direction of motion by the distance the object moves. In this case, since the cart is being moved up the ramp, the force applied in the direction of motion is equal to the component of the applied force parallel to the displacement.
Step 1: Calculate the component of the applied force parallel to the displacement.
Force_parallel = force * sin(theta)
Step 2: Calculate the work out.
Work Out = Force_parallel * distance
Work Out = Force_parallel * displacement * cos(theta)
IMA (Ideal Mechanical Advantage):
The ideal mechanical advantage is defined as the ratio of the distance traveled by the input force to the distance traveled by the output force. In this case, the input force is the applied force, and the output force is the weight of the cart and the boxes.
IMA = distance input / distance output
IMA = displacement / distance
AMA (Actual Mechanical Advantage):
The actual mechanical advantage is defined as the ratio of the output force to the input force. In this case, the output force is the weight of the cart and the boxes, and the input force is the applied force.
AMA = force output / force input
AMA = weight / force
Efficiency:
Efficiency is defined as the ratio of useful work output to the total work input. In this case, the useful work output is the work done on the cart, while the total work input is the work done by the student.
Efficiency = work out / work in
Power:
Power is the rate at which work is done. It can be calculated by dividing the work done by the time taken.
Power = work / time
To find the numerical answers, you'll need to plug in the given values into the formulas and perform the calculations.