In which of the following situations is the most work done on the object?
A. Holding a 50 kg object.
B. Carrying a 30 kg object down a 40 m long hallway.
C. Lifting a 20 kg object 1 m up.
D. Carrying a 15 kg object up a flight of stairs.
E. Lowering a 25 kg object from a second story balcony to the ground
My answer is C.
To determine the situation in which the most work is done on the object, we need to calculate the work done in each scenario. The work done on an object is calculated using the formula:
Work = Force x Distance x cos(theta)
Where:
- Force is the force applied on the object
- Distance is the distance over which the force is applied
- Theta is the angle between the force and the direction of displacement.
Let's calculate the work done in each situation:
A. Holding a 50 kg object:
In this scenario, no work is done since there is no displacement. The object is not moving, so the distance is zero. Therefore, the work done is zero.
B. Carrying a 30 kg object down a 40 m long hallway:
In this situation, work is done against gravity and the force of friction. To simplify the calculation, let's assume no friction.
The force applied to lift the object against gravity is equal to the weight of the object, which is given by:
Force = mass x gravity
Force = 30 kg x 9.8 m/s^2
Force ≈ 294 N
The distance over which the force is applied is 40 m.
Theta is the angle between the force of gravity and the direction of displacement, which is 0 degrees since the object is being moved vertically downwards.
Using the formula:
Work = Force x Distance x cos(theta)
Work = 294 N x 40 m x cos(0)
Work = 11,760 joules
C. Lifting a 20 kg object 1 m up:
In this situation, work is done against gravity.
Following the same steps, the force applied to lift the object against gravity is equal to the weight of the object:
Force = mass x gravity
Force = 20 kg x 9.8 m/s^2
Force = 196 N
The distance over which the force is applied is 1 m.
Theta is the angle between the force of gravity and the direction of displacement, which is 0 degrees since the object is being moved vertically upwards.
Using the formula:
Work = Force x Distance x cos(theta)
Work = 196 N x 1 m x cos(0)
Work = 196 joules
D. Carrying a 15 kg object up a flight of stairs:
In this scenario, work is done against gravity.
Using the same approach as above, the force applied to lift the object against gravity is equal to the weight of the object:
Force = mass x gravity
Force = 15 kg x 9.8 m/s^2
Force = 147 N
The distance over which the force is applied varies depending on the number of stairs. Let's assume there are 10 stairs, and each is 0.2 m high. So the total vertical displacement is:
Distance = 10 stairs x 0.2 m/stair
Distance = 2 m
Theta is the angle between the force of gravity and the direction of displacement, which is 0 degrees since the object is being moved vertically upwards.
Using the formula:
Work = Force x Distance x cos(theta)
Work = 147 N x 2 m x cos(0)
Work = 294 joules
E. Lowering a 25 kg object from a second-story balcony to the ground:
In this scenario, work is done by gravity.
The force applied to lower the object is equal to the weight of the object:
Force = mass x gravity
Force = 25 kg x 9.8 m/s^2
Force = 245 N
The distance over which the force is applied is the vertical distance between the second-story balcony and the ground. Let's assume it is 5 m.
Theta is the angle between the force of gravity and the direction of displacement, which is 180 degrees since the object is being lowered vertically downwards.
Using the formula:
Work = Force x Distance x cos(theta)
Work = 245 N x 5 m x cos(180)
Work = -1225 joules (negative sign indicates work done by gravity)
Based on the calculation, the situation in which the most work is done on the object is scenario B, carrying a 30 kg object down a 40 m long hallway. In this scenario, 11,760 joules of work are done.
To determine which situation involves the most work done on the object, we need to understand the definition of work. Work is calculated as the product of force applied on an object and the displacement of the object in the direction of the applied force. Mathematically, work (W) is given by the formula W = F × d × cosθ, where F is the force applied, d is the displacement, and θ is the angle between the force vector and the displacement vector.
Let's analyze each situation:
A. Holding a 50 kg object: In this case, no work is done. The object is not moving, so there is no displacement.
B. Carrying a 30 kg object down a 40 m long hallway: To carry the object down the hallway, a horizontal force is required. Since the displacement is in the same direction as the force, work is done. Thus, work is done in this situation.
C. Lifting a 20 kg object 1 m up: Lifting the object requires exerting an upward force against gravity. The displacement is vertical, directly opposite to the force applied. Consequently, work is done in lifting the object.
D. Carrying a 15 kg object up a flight of stairs: Similar to the previous situation, carrying the object up the stairs involves exerting an upward force against gravity. The displacement is vertical, opposing the force. Consequently, work is done in carrying the object.
E. Lowering a 25 kg object from a second-story balcony to the ground: Lowering the object involves applying a downward force, but the displacement is vertical and in the opposite direction of the force. Therefore, work is still done, just with a negative value.
In summary, the situations where work is done on the object are B, C, D, and E. However, to determine which one involves the most work, we need additional information such as the magnitude of the force applied.