A boy pushes a lawn mower with a mas of 17.9 kg starting from rest across a horizontal lawn by applying a force of 32.9N straight along the handle, which is inclined at an agle of 35.1 degrees above the horizontal. The magnitude of the mower's accelerations is 1.37m/s^2, which lasts for 0.58 s after which the mower moves at a constant velocity. Determine the magnitude of:

A)the normal force on the mower
B)the frictional force on the mower
C)the maximum velocity
d) the force applied by the boy needed to maintain the constant velocity.

Please do not just "drop off" problems. Show your work. Do you know what "the normal force" means? It is the component of the applied force that is perpendicular to the ground. Start by calculating that.

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To solve this problem, we will use Newton's second law of motion:

F = ma

where F is the force, m is the mass, and a is the acceleration.

A) The normal force on the mower can be determined by balancing the vertical forces. The normal force is equal in magnitude and opposite in direction to the force of gravity acting on the mower. The force of gravity can be calculated using the equation:

F_gravity = mg

where m is the mass of the mower and g is the acceleration due to gravity (9.8 m/s^2). So:

F_gravity = (17.9 kg)(9.8 m/s^2) = 175.42 N

Since the mower is on a horizontal surface, the normal force should be equal in magnitude and opposite in direction. Therefore, the magnitude of the normal force is also 175.42 N.

B) The frictional force on the mower can be determined using the equation:

F_friction = μ * F_normal

where μ is the coefficient of friction between the mower and the ground. Since the mower is moving at a constant velocity, the frictional force must be equal in magnitude and opposite in direction to the force applied by the boy to maintain the constant velocity. Therefore, we can use the force applied by the boy to calculate the frictional force.

C) The maximum velocity can be determined by analyzing the acceleration phase of the mower's motion. We are given the mower's acceleration (1.37 m/s^2) and the time it takes to reach this acceleration (0.58 s). We can use the following kinematic equation to find the maximum velocity:

v = u + at

where v is the final velocity, u is the initial velocity (0 m/s since it starts from rest), a is the acceleration, and t is the time.

v = (0 m/s) + (1.37 m/s^2)(0.58 s) = 0.7956 m/s

Therefore, the maximum velocity is approximately 0.7956 m/s.

D) The force applied by the boy needed to maintain the constant velocity can be determined by balancing the horizontal forces. Since the mower is moving at a constant velocity, the net force in the horizontal direction must be zero. Therefore, the force applied by the boy is equal in magnitude and opposite in direction to the frictional force.

Once we calculate the frictional force (as explained in part B), we will have the magnitude of the force applied by the boy needed to maintain the constant velocity.