How much work is done by gravity?
Understand the Problem
The question asks about the amount of work done by gravity when a crate is pushed horizontally. The context includes the mass of the crate and the distance it is moved, but the work done by gravity would be related to vertical displacement, which is absent here.
Answer
The work done by gravity is \( W_g = 0 \, \text{J} \).
Answer for screen readers
The work done by gravity is ( W_g = 0 , \text{J} ).
Steps to Solve
- Understanding Work Done by Gravity
The work done by a force is calculated using the formula:
$$ W = F \cdot d \cdot \cos(\theta) $$
where ( W ) is the work done, ( F ) is the force applied, ( d ) is the distance moved, and ( \theta ) is the angle between the force and the direction of motion.
- Identify the Forces Involved
In this scenario, the force due to gravity ( F_g ) is:
$$ F_g = m \cdot g $$
where:
- ( m = 28.9 , \text{kg} ) (mass of the crate)
- ( g = 9.81 , \text{m/s}^2 ) (acceleration due to gravity)
Now, calculate ( F_g ):
$$ F_g = 28.9 , \text{kg} \times 9.81 , \text{m/s}^2 $$
- Determining the Angle
Since the crate is pushed horizontally on a level floor, the angle ( \theta ) between the gravitational force (which acts vertically downward) and the horizontal displacement is ( 90^\circ ).
- Calculating the Work Done by Gravity
Substituting into the work formula:
$$ W_g = F_g \cdot d \cdot \cos(90^\circ) $$
Since ( \cos(90^\circ) = 0 ), we simplify the equation to:
$$ W_g = F_g \cdot d \cdot 0 = 0 $$
This shows that the work done by gravity on the crate while it is pushed horizontally is zero.
The work done by gravity is ( W_g = 0 , \text{J} ).
More Information
The work done by gravity is zero in this case because there is no vertical displacement. Work is only done when there is a component of movement in the direction of the force.
Tips
- Confusing vertical and horizontal displacement: Remember that gravity acts vertically while the crate is moved horizontally; therefore, no work is done by gravity in this scenario.
- Not considering the angle: Forgetting to set the angle to ( 90^\circ ) can lead to incorrect calculations since this results in a cosine of zero.
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