Question

A roofing shingle elevator is lifting a 30.0-kg package to the top of a building at constant speed. The angle between the elevator track and the horizontal is 75∘. The power of the elevator is 800 W. Part A Determine the vertical component of the speed with which the package is moving up. Assume no friction is exerted by the incline surface on the package.

Answer 1

To determine the vertical component of the speed with which the package is moving up, we can use the given angle and the elevator's power to calculate the force exerted by the elevator. Then, we can calculate the vertical component of the speed using the formula Vertical Speed = Velocity * sin(angle).

Step-by-step explanation:

To determine the vertical component of the speed with which the package is moving up, we need to calculate the velocity of the package in the vertical direction. Since the package is moving at constant speed, the vertical component of its velocity is also constant. We can use the given angle and the elevator's power to find the vertical component of the speed.

First, we need to calculate the force exerted by the elevator to lift the package. The force can be calculated using the formula:

Force = Power / Velocity

Since the package is moving at constant speed, the force exerted by the elevator is equal to the weight of the package. We can calculate the weight using the formula:

Weight = Mass * Gravitational Acceleration

Finally, we can calculate the vertical component of the speed using the formula:

Vertical Speed = Velocity * sin(angle)

Answer 2

Step-by-step explanation:

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