A man carries a 4.4-kg luggage while walking 2 meters. What is the work done by the man's hand on the luggage?
none, no force in direction of motion.
To calculate the work done by the man's hand on the luggage, we can use the formula:
Work (W) = Force (F) x Distance (d) x cos(theta)
In this case, the force exerted by the man's hand is equal to the weight of the luggage. The weight is calculated using the formula:
Weight (W) = Mass (m) x Gravitational Acceleration (g)
Given:
Mass (m) = 4.4 kg
Gravitational Acceleration (g) = 9.8 m/s^2 (approximately)
First, let's calculate the weight of the luggage:
Weight (W) = 4.4 kg x 9.8 m/s^2 = 43.12 N (approximately)
Since the luggage is being carried horizontally, the angle between the applied force and the displacement is 0 degrees. Therefore, the cosine of the angle (cos(theta)) is 1.
Now, we can calculate the work done by the man's hand:
Work (W) = 43.12 N x 2 m x cos(0) = 43.12 N x 2 m x 1 = 86.24 Joules (approximately)
So, the work done by the man's hand on the luggage is approximately 86.24 Joules.
To find the work done by the man's hand on the luggage, we can use the formula for work:
Work = Force × Displacement × Cosine(θ)
In this case, the force exerted by the man's hand on the luggage is equal to the weight of the luggage. The weight can be calculated using the following formula:
Weight = mass × acceleration due to gravity
Let's substitute the given values into the formulas and solve for the work:
Mass of the luggage = 4.4 kg
Acceleration due to gravity = 9.8 m/s² (approximately)
Weight = 4.4 kg × 9.8 m/s² ≈ 43.12 N
Now we have the force exerted by the man's hand (43.12 N) and the displacement (2 meters). Since the work is done in the same direction as the displacement, the angle (θ) between the force and displacement is 0 degrees.
Now we plug the values into the work formula:
Work = 43.12 N × 2 m × Cosine(0°)
Since the cosine of 0 degrees is equal to 1, the calculation simplifies to:
Work = 43.12 N × 2 m × 1
= 86.24 N⋅m
Therefore, the work done by the man's hand on the luggage is approximately 86.24 N⋅m (Newton-meters), also known as joules (J).