Question

A machine is designed to push packages into a storage container for overseas shipping. on a certain package, the machine applies a pushing force at an angle of 35° above horizontal. The ramp that the package slides up is 22° above horizontal. If the ramp is 4.11 m long, and the machine performs 1150 J of work, how much force does the machine apply to the package

Answer 1

The force applied by the machine to the package is 349.36 N.

Step-by-step explanation:

To calculate the force applied by the machine to the package, we need to first calculate the work done by the machine. The work done can be calculated using the formula:

Work = Force x Distance x cos(theta)

Where: Force is the applied force, Distance is the length of the ramp, and theta is the angle between the applied force and the horizontal.

In this case, the work done is given as 1150 J, the distance is 4.11 m, and the angle theta is 35° above horizontal.

Rearranging the formula, we can solve for the force:

Force = Work / (Distance x cos(theta))

Plugging in the given values:

Force = 1150 J / (4.11 m x cos(35°))

Calculating the value:

Force = 1150 J / (4.11 m x 0.819)

Force = 349.36 N

Therefore, the machine applies a force of 349.36 N to the package.