A person pushes a 10.0 kg lawn mower at constant speed with a force of 80.0 N di

Question

A person pushes a 10.0 kg lawn mower at constant speed with a force of 80.0 N directed along the handle, which is at an angle of ? = 40.0 to the horizontal as shown. Hint: Draw the free-body diagram showing all forces acting on the mower and write Net Force equations. (a) Calculate the horizontal frictional force on the mower. 1. N (b) Calculate the normal force exerted vertically upward on the mower by the ground. 2. N (c) Calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.1 m/s in 2.0 seconds (assuming the same frictional force). 3. N

Explanation / Answer

Force = F = 80 Newton
angle = 40 degrees

mass = m = 10 kg

Now horizontal Component of Force F = Fx = Fcos

= 80cos(40)

= 61.28 Newtons

Now, given that the mower runs at constant velocity,

therefore the forces balance each other.

Now,

Fx = f ( fis frictional Force)

a.

Frictional Force f = Fx = 61.28 Newtons

b.

Normal Force Exerted = N = mg + Fy

= 10 x 9.8 + 80sin(40)

= 149.42 Newtons

c.

initial speed u= 0

final speed v= 1.1 m/s

time t = 2seconds

Acceleration = (v-u)/t = 0.55 m/s^2

we have, considering forces along horizontal axis,

ma = F cos - f

10x 0.55 = F cos(40) - 61.28

Force F = 87.175 Newtons

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