A person pushes a 11.0 kg lawn mower at constant speed with a force of 82.0 N directed along the handle, which is at an angle of θ = 45.0° to the horizontal.Calculate the normal force exerted vertically upward on the mower by the ground.
well, the normal force has to overcome the weight of the mower, mg, plus the downward force of pushing, which is 82Cos45.
add them
To find the normal force exerted vertically upward on the mower by the ground, we need to consider the forces acting on the mower and apply Newton's second law of motion.
1. Draw a free-body diagram: Start by drawing a diagram showing all the forces acting on the mower. In this case, we have:
- The weight of the mower acting vertically downward (mg).
- The force of gravity acting vertically downward (mg).
- The force applied by the person pushing the mower (F) at an angle of 45.0° to the horizontal.
- The normal force exerted by the ground upward (N).
2. Resolve forces into components: Since the applied force is at an angle to the horizontal, we need to resolve it into its horizontal and vertical components. The vertical component of the applied force (F_y) will be responsible for balancing the weight of the mower, while the horizontal component (F_x) will not affect the normal force.
- F_y = F * sin(θ)
- F_x = F * cos(θ)
3. Apply Newton's second law: Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration (F_net = ma). In this case, since the mower is moving at a constant speed, the acceleration is zero. Therefore, the sum of all the vertical forces must be zero.
- F_net_y = F_y - mg - N = 0
4. Solve for the normal force: Rearrange the equation to solve for the normal force (N).
- N = F_y - mg
5. Substitute the given values: Plug in the values given in the problem to calculate the normal force.
- F = 82.0 N
- θ = 45.0°
- m = 11.0 kg
- g = 9.8 m/s²
Calculate the vertical component of the applied force:
- F_y = F * sin(θ)
Calculate the normal force:
- N = F_y - mg
6. Compute the normal force: Substitute the values into the equation and calculate the normal force.
- F_y = 82.0 N * sin(45.0°)
- N = (82.0 N * sin(45.0°)) - (11.0 kg * 9.8 m/s²)
After evaluating the equation, you will find the value of the normal force exerted vertically upward on the mower by the ground.