Calculating Force to Accelerate Lawn Mower: Newton's 2nd Law

[kgood5885]

I figured out the horizontal friction force, Fpx to be 55.11 N and the normal force exerted vertically to be 190.8 N. And the other info given is F = 84 the lawn mower has a mass of 13 kg and moves at a constant speed. The lawn mower is at an angle of 49 degrees to the horizontal. I need to determine 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).
Do I use the equation 84 cos 49 + F (friciton) = ma? Or how do I set up this problem?

 

[lightgrav]

If the person's Force is along a 49 degree handle
(while the lawn mower itself is on level?)
the person's force will increase the N required,
and might increase the friction Force.

Does your friction stay at 84 cos(49) ?
then get Fx_extra = ma_x

 

[quicknote]

To calculate the force needed to accelerate the lawn mower, we can use Newton's Second Law, which states that force is equal to mass times acceleration (F=ma). In this case, the mass of the lawn mower is given as 13 kg and the desired acceleration is 1.3 m/s^2. Therefore, the force needed to accelerate the lawn mower is 13 kg x 1.3 m/s^2 = 16.9 N.

However, we also need to take into account the friction force and the normal force exerted on the lawn mower. Since the lawn mower is at an angle of 49 degrees to the horizontal, we need to consider the components of the forces in the horizontal and vertical directions.

To calculate the horizontal component of the friction force, we can use the formula Fpx = Fp x cos θ, where Fp is the total friction force and θ is the angle between the friction force and the horizontal direction. In this case, we have Fp = 55.11 N and θ = 49 degrees, so Fpx = 55.11 N x cos 49 = 35.5 N.

Next, we can calculate the normal force exerted on the lawn mower using the formula Fny = mgcosθ, where m is the mass of the lawn mower, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the slope. In this case, we have m = 13 kg, g = 9.8 m/s^2, and θ = 49 degrees, so Fny = 13 kg x 9.8 m/s^2 x cos 49 = 90.8 N.

Now, we can use the equation F = ma to set up the problem. We know that the total force (F) is equal to the sum of the forces in the horizontal direction (Fpx) and the force needed to accelerate the lawn mower (16.9 N). Therefore, we have F = Fpx + 16.9 N. We can substitute the values we calculated for Fpx and solve for the unknown force as follows:

F = 35.5 N + 16.9 N = 52.4 N

Therefore, the person must exert a force of 52.4 N on the lawn mower to accelerate it from rest to 1.3 m/s in