Solving Lawn Mower Problem: Retarding Force, Normal Force, Acceleration

[trixid]

A person pushes a 14.5 kg lawn mower at a constant speed with a force of 88.0 N directed along the handle, which is at an angle of 45.0 degrees to the horizontal. (a) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal retarding force on the mower, then (c) the nomal force exerted vertically upward on the mower by the ground, and (d) the force the person must exert on the lawn mower to accelerate it from rest to 1.5 m/s in 2.5 seconds (assuming the same retarding force).

I got the free body diagram but I'm lost on the rest of it.

 

[nolachrymose]

For (b), the "retarding" force (that's an odd way of wording I've never seend) is basically that which opposes the motion of the lawn mower. Do you know which force that is, and then how to calculate it?
For (c), you know that the normal force and the gravitational force are equal and opposite forces. Use that fact to find the normal force.
For (d), find the acceleration of the object and then input into the ubiquitous equation F=ma.

Hope that helps! ;)

 

[wais]

(a) The free-body diagram would show the following forces acting on the lawn mower:
1. The force applied by the person pushing the mower (88.0 N at 45.0 degrees to the horizontal)
2. The weight of the mower (mg, directed downwards)
3. The normal force exerted by the ground on the mower (perpendicular to the surface)
4. The retarding force (opposing the direction of motion)

(b) To calculate the horizontal retarding force, we need to use the equation F = ma, where F is the net force, m is the mass, and a is the acceleration. Since the mower is moving at a constant speed, the acceleration is 0. Therefore, the net force must also be 0. This means that the horizontal retarding force is equal in magnitude to the force applied by the person, but in the opposite direction. So, the horizontal retarding force is 88.0 N.

(c) The normal force exerted by the ground on the mower can be calculated using the same equation as above, F = ma. In this case, the net force in the vertical direction is 0, since the mower is not accelerating in that direction. Therefore, the normal force must be equal in magnitude to the weight of the mower, which is given as 14.5 kg x 9.8 m/s^2 = 141.1 N.

(d) To calculate the force required to accelerate the mower, we can use the equation F = ma again. This time, the net force is not 0, since the mower is accelerating. The mass is still 14.5 kg, and the acceleration is given as 1.5 m/s^2. Therefore, the force needed to accelerate the mower is 14.5 kg x 1.5 m/s^2 = 21.75 N. However, since the same retarding force of 88.0 N is still acting on the mower, the person would actually need to exert a force of 88.0 N + 21.75 N = 109.75 N in order to accelerate the mower.