Q1. What force must the deltoid muscle provide to keep the arm in this position?

Background

Topic: Static Equilibrium and Torque

This question tests your understanding of how muscles generate forces to maintain static equilibrium in the human body, specifically using torque calculations.

Key Terms and Formulas

• Torque ():

• Static Equilibrium: The sum of all torques about any point must be zero.

• Force of gravity:

Step-by-Step Guidance

1. Identify the forces acting on the arm: the weight of the arm () and the force from the deltoid muscle ().

2. Calculate the torque due to the weight of the arm about the shoulder joint. Use m (distance to center of mass) and kg.

3. Set up the torque equation for static equilibrium: .

4. Express the torque from the deltoid muscle using its force, distance ( m), and angle ().

Try solving on your own before revealing the answer!

Q2. By what factor does this force exceed the weight of the arm?

Background

Topic: Ratio of Forces

This question asks you to compare the force generated by the deltoid muscle to the actual weight of the arm.

Key Terms and Formulas

• Weight of the arm:

• Ratio:

Step-by-Step Guidance

1. Calculate the weight of the arm using kg and m/s.

2. Use the previously calculated deltoid force.

3. Set up the ratio formula: .

Try solving on your own before revealing the answer!

Q3. What is the critical angle for the unloaded double-decker bus?

Background

Topic: Stability and Center of Gravity

This question tests your understanding of how the center of gravity and track width affect the tipping angle of a vehicle.

Key Terms and Formulas

• Critical angle ():

• = track width, = height of center of gravity

Step-by-Step Guidance

1. Identify the values: m, m (unloaded).

2. Set up the formula: .

3. Calculate and then use the arctangent function to find .

Try solving on your own before revealing the answer!

Q4. What is the force required to support the wheelbarrow?

Background

Topic: Static Equilibrium and Torque

This question tests your ability to use torque and equilibrium to find the force needed to support a load.

Key Terms and Formulas

• Torque ():

• Static Equilibrium:

Step-by-Step Guidance

1. Identify the forces: weight of the wheelbarrow and load, and the supporting force at the handles.

2. Calculate the torque due to the weight about the axle using m and kg.

3. Set up the equilibrium equation: .

Try solving on your own before revealing the answer!

Q5. What is the tension in the cable supporting the sign?

Background

Topic: Static Equilibrium and Forces

This question tests your ability to analyze forces in a system in static equilibrium, specifically using trigonometry to resolve tensions.

Key Terms and Formulas

• Force components: and

• Static Equilibrium: and

Step-by-Step Guidance

1. Identify the forces: weight of the sign ( kg), tension in the cable, and the angle ().

2. Set up the equilibrium equations for vertical and horizontal forces.

3. Use the torque equation about the pivot point to solve for the tension in the cable.

Try solving on your own before revealing the answer!

Q6. How much work is done by the weight of the piano as it is lowered?

Background

Topic: Work and Energy

This question tests your understanding of work done by a force over a distance, specifically gravitational work.

Key Terms and Formulas

• Work ():

• Weight:

Step-by-Step Guidance

1. Identify the mass of the piano ( kg) and the distance lowered ( m).

2. Calculate the weight: .

3. Set up the work formula: .

Try solving on your own before revealing the answer!