A 4600 kg helicopter accelerates upward at 2.0 mls” _ Determine the lift force exerted on the propellers by the air: Make quantitative force diagram: Write net force equation for the axis along which forces are not balanced: The maximum force that grocery bag can withstand without ripping is 250 N. Suppose that the bag is filled with 20 kg of groceries and lifted with an acceleration of 5.0 m/s? Do the groceries stay in the bag? Make # quantitative force diagram. Write net force equation for the axis along which forces are not balanced
The Correct Answer and Explanation is:
Part 1: Helicopter Lift Force Calculation
Given:
- Mass of helicopter, m = 4600 kg
- Acceleration upward, a = 2.0 m/s²
- Gravitational force, Fg = m × g = 4600 kg × 9.8 m/s² = 45,080 N
Quantitative Force Diagram:
- Upward Force: Lift Force (FL)
- Downward Force: Gravitational Force (Fg)
Net Force Equation (Vertical Axis):
∑F = FL – Fg = m × a
Substitute known values:
FL – 45,080 N = 4600 kg × 2.0 m/s²
FL – 45,080 N = 9,200 N
FL = 9,200 N + 45,080 N = 54,280 N
Lift Force Exerted: 54,280 N upward
Part 2: Grocery Bag Problem
Given:
- Maximum force bag can withstand = 250 N
- Mass of groceries, m = 20 kg
- Acceleration upward, a = 5.0 m/s²
- Gravitational force, Fg = m × g = 20 kg × 9.8 m/s² = 196 N
Quantitative Force Diagram:
- Upward Force: Tension in the bag (T)
- Downward Force: Gravitational Force (Fg)
Net Force Equation (Vertical Axis):
∑F = T – Fg = m × a
Substitute known values:
T – 196 N = 20 kg × 5.0 m/s²
T – 196 N = 100 N
T = 100 N + 196 N = 296 N
Analysis:
The tension required to lift the groceries with the given acceleration is 296 N, but the bag can only withstand 250 N. Therefore, the groceries do not stay in the bag, the bag will rip.
Explanation:
For the helicopter, the total lift force must overcome both the gravitational pull and provide additional force for upward acceleration. By using Newton’s Second Law (F = ma), we combine gravitational force with the force due to acceleration to find the total lift.
Similarly, in the grocery bag scenario, the bag not only has to support the weight of the groceries but also provide extra force for the upward acceleration. The required tension exceeds the bag’s maximum limit, so the bag fails. Quantitative force diagrams help visualize these situations by clearly representing all acting forces, allowing for precise application of Newton’s laws to solve for unknown quantities.
