Question

A person pushes a lawnmower at a constant speed across their yard. the mower has a mass of 50 kg 50 kg50, start text, space, k, g, end text, and there is a friction force between the lawn mower and ground of 100 n 100 n100, start text, space, n, end text. the person pushes into the end of the handle which makes an angle of 25 � 25�25, degree below the horizontal. assume the yard is level. a person pushes a lawnmower on a flat grassy surface. the angle made between the horizontal and the right side of the handle of the lawnmower is labeled twenty five degrees. a person pushes a lawnmower on a flat grassy surface. the angle made between the horizontal and the right side of the handle of the lawnmower is labeled twenty five degrees. determine the magnitude of the normal force the ground exerts on the mower. give your an

Answer 1

To calculate the normal force on the mower, the weight of the mower is needed along with the vertical component of the force applied by the person. With these values one can then subtract the vertical force from the total weight to find the normal force.

Step-by-step explanation:

To determine the magnitude of the normal force the ground exerts on the mower, we need to consider the forces acting on the lawnmower in the vertical direction. Since the mower is moving at constant speed, the net force in the horizontal direction is zero, which means the force exerted by the person in the horizontal component must be equal to the force of friction. However, the person exerts a force at an angle, so we need to calculate the vertical component of this force.

The vertical component of the applied force acts against gravity and affects the normal force. If F is the force exerted by the person and θ is the angle below the horizontal, the vertical component is F sin(θ). The weight of the mower (W) is the product of its mass (m) and gravitational acceleration (g), W = m * g. The normal force (N) plus the vertical component of the pushing force must balance the weight of the mower, so N = W - F sin(θ). Without the magnitude of the force (F) that the person applies, we cannot calculate the exact normal force. In general, however, the normal force is the weight of the lawnmower reduced by the vertical component of the applied force.

Answer 2

The normal force the ground exerts on the mower can be approximated by the mower's weight, which is calculated as the product of its mass (50 kg) and the acceleration due to gravity (9.8 m/s²), resulting in a normal force of approximately 490 N.

Step-by-step explanation:

To determine the magnitude of the normal force the ground exerts on the mower, it is essential to consider two forces. First, the weight of the mower due to gravity (W = m * g, where m is the mass and g is the acceleration due to gravity which is approximately 9.8 m/s²). Second, the vertical component of the pushing force, which can be calculated using trigonometry (F_y = F * sin(θ), where F is the pushing force and θ is the angle).

If the mower is moving at a constant speed and the yard is level, then the net vertical force is zero, meaning the normal force (N) must counteract both the weight of the mower and the vertical component of the push. Since the exact pushing force (F) is not given, and assuming there's no upward acceleration, the normal force can be primarily attributed to the weight of the mower. Therefore, N ≈ m * g. For a 50 kg mower, N ≈ 50 kg * 9.8 m/s² = 490 N.