How Do You Apply Newton's Laws to Calculate Forces on a Lawn Mower?

[kgood5885]

A person pushes a 13.0 kg lawn mower at constant speed with a force of 84.0 N directed along the handle, which is at an angle of = 49.0° to the horizontal.

(a) Calculate the horizontal retarding force on the mower

(b) Calculate the normal force exerted vertically upward on the mower by the ground.

(c) Calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.3 m/s in 2.0 seconds (assuming the same retarding force).

Here's what I have so far...

a) FPx = 84 cos 49 = 55.11 N
FPy = 84 sin 49 = 63.396 N
∑ F = ma
N – mg = ma
N = mg
= 13.0(9.8)
= 127.4 N

b) Ffr = (coefficient of friction)FN
= (0.30)(127.4)
= 38.22 N
c) I have no idea where to even start for this question!

Please help!

 

[Doc Al]

Here's what I have so far...

a) FPx = 84 cos 49 = 55.11 N
FPy = 84 sin 49 = 63.396 N
∑ F = ma
N – mg = ma
N = mg
= 13.0(9.8)
= 127.4 N

All you need to answer this part is to realize that the net horizontal force must be zero. The retarding force must balance the horizontal component of the applied force.

b) Ffr = (coefficient of friction)FN
= (0.30)(127.4)
= 38.22 N

For this part, all you need to find is the normal force. (Where did you get the coefficient of friction?) This time use the fact that the net vertical force must be zero. (Hint: There are three vertical forces.)

c) I have no idea where to even start for this question!

To get an acceleration, the net horizontal force must be greater than zero. Apply Newton's 2nd law.

 

[quicknote]

I would like to commend you on your calculations so far. You have correctly applied Newton's laws to determine the retarding force and normal force on the lawn mower. To calculate the force required to accelerate the lawn mower, we can use the equation F = ma, where F is the net force, m is the mass, and a is the acceleration. In this case, we know the mass of the lawn mower (13.0 kg) and the acceleration (1.3 m/s^2), so we can rearrange the equation to solve for the net force, which is the force that the person must exert on the lawn mower.

F = ma
F = (13.0 kg)(1.3 m/s^2)
F = 16.9 N

Therefore, the person must exert a force of 16.9 N on the lawn mower to accelerate it from rest to 1.3 m/s in 2.0 seconds, assuming the same retarding force of 38.22 N. This means that the person must push with a force of 16.9 N plus the retarding force of 38.22 N, for a total force of 55.11 N, in order to achieve this acceleration.

In summary, by applying Newton's laws, we can determine the retarding force and normal force on the lawn mower, as well as the force required to accelerate it. These calculations are essential for understanding the motion and forces involved in this scenario.