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Find the magnitude of the vertical force this lawnmower exerts on the lawn. Answer in units of N.

Find the magnitude of the vertical force this lawnmower exerts on the lawn. Answer in units of N.

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**Physics Problem: Calculating the Normal Force** **Problem Statement:** A woman pushes a 29 kg lawnmower at a steady speed. She exerts a 150 N force in a direction 26° below the horizontal. The acceleration of gravity is 9.8 m/s². **Hint:** Solve for FORCE NORMAL here. In this problem, we are asked to find the normal force exerted on the lawnmower. To solve this, consider the following steps: 1. **Identify the Forces:** - The weight of the lawnmower (gravitational force) acts downward. - The applied force by the woman has a horizontal and vertical component. - The normal force acts upward perpendicular to the ground. 2. **Components of the Applied Force:** - The horizontal component is \( F_{horizontal} = 150 \, \text{N} \cdot \cos(26°) \). - The vertical component is \( F_{vertical} = 150 \, \text{N} \cdot \sin(26°) \). 3. **Determine the Normal Force:** - The normal force can be found by balancing the vertical forces. - Sum of vertical forces \( = \text{Normal force} + F_{vertical} = \text{Weight} \). - Solve the equation for the normal force. This setup allows you to determine the normal force using the principles of Newton's laws of motion and vector decomposition of forces.
Transcribed Image Text:**Physics Problem: Calculating the Normal Force** **Problem Statement:** A woman pushes a 29 kg lawnmower at a steady speed. She exerts a 150 N force in a direction 26° below the horizontal. The acceleration of gravity is 9.8 m/s². **Hint:** Solve for FORCE NORMAL here. In this problem, we are asked to find the normal force exerted on the lawnmower. To solve this, consider the following steps: 1. **Identify the Forces:** - The weight of the lawnmower (gravitational force) acts downward. - The applied force by the woman has a horizontal and vertical component. - The normal force acts upward perpendicular to the ground. 2. **Components of the Applied Force:** - The horizontal component is \( F_{horizontal} = 150 \, \text{N} \cdot \cos(26°) \). - The vertical component is \( F_{vertical} = 150 \, \text{N} \cdot \sin(26°) \). 3. **Determine the Normal Force:** - The normal force can be found by balancing the vertical forces. - Sum of vertical forces \( = \text{Normal force} + F_{vertical} = \text{Weight} \). - Solve the equation for the normal force. This setup allows you to determine the normal force using the principles of Newton's laws of motion and vector decomposition of forces.
### Educational Explanation: Calculating the Vertical Force Exerted by a Lawnmower **Problem Statement:** We need to determine the magnitude of the vertical force that a lawnmower, which has a mass of 29 kg, exerts on the lawn. Given values include a force of 150 N applied at an angle of 26° above the horizontal. The answer should be provided in units of Newtons (N). **Diagram Explanation:** - The diagram shows a lawnmower represented by a rectangle labeled "29 kg." - There is an arrow pointing diagonally upward to the right, labeled "150 N" at an angle of 26° from the horizontal. **Solution Approach:** To find the vertical component of the force exerted by the lawnmower: 1. **Identify the Applied Force:** - Total applied force is 150 N at an angle of 26°. 2. **Calculate the Vertical Component of the Force:** - Use the formula for the vertical component: \[ F_{\text{vertical}} = F \cdot \sin(\theta) \] where \( F = 150 \, \text{N} \) and \( \theta = 26^\circ \). 3. **Calculate the Gravitational Force:** - The gravitational force acting on the lawnmower is given by: \[ F_{\text{gravity}} = m \cdot g \] where \( m = 29 \, \text{kg} \) and \( g \approx 9.81 \, \text{m/s}^2 \). 4. **Determine the Net Vertical Force:** - The net vertical force on the lawn would then be: \[ F_{\text{net, vertical}} = F_{\text{gravity}} - F_{\text{vertical}} \] By solving these calculations, you can find the magnitude of the vertical force that the lawnmower exerts on the lawn.
Transcribed Image Text:### Educational Explanation: Calculating the Vertical Force Exerted by a Lawnmower **Problem Statement:** We need to determine the magnitude of the vertical force that a lawnmower, which has a mass of 29 kg, exerts on the lawn. Given values include a force of 150 N applied at an angle of 26° above the horizontal. The answer should be provided in units of Newtons (N). **Diagram Explanation:** - The diagram shows a lawnmower represented by a rectangle labeled "29 kg." - There is an arrow pointing diagonally upward to the right, labeled "150 N" at an angle of 26° from the horizontal. **Solution Approach:** To find the vertical component of the force exerted by the lawnmower: 1. **Identify the Applied Force:** - Total applied force is 150 N at an angle of 26°. 2. **Calculate the Vertical Component of the Force:** - Use the formula for the vertical component: \[ F_{\text{vertical}} = F \cdot \sin(\theta) \] where \( F = 150 \, \text{N} \) and \( \theta = 26^\circ \). 3. **Calculate the Gravitational Force:** - The gravitational force acting on the lawnmower is given by: \[ F_{\text{gravity}} = m \cdot g \] where \( m = 29 \, \text{kg} \) and \( g \approx 9.81 \, \text{m/s}^2 \). 4. **Determine the Net Vertical Force:** - The net vertical force on the lawn would then be: \[ F_{\text{net, vertical}} = F_{\text{gravity}} - F_{\text{vertical}} \] By solving these calculations, you can find the magnitude of the vertical force that the lawnmower exerts on the lawn.
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