Respuesta :
Answer:
58.4 W
Explanation:
The speed of the lawnmower is constant: this means that its acceleration is zero, so the net force on it is zero.
The equation of the forces along the two directions therefore are:
- Perpendicular to the floor: [tex]F sin \theta + R -mg =0[/tex]
- Parallel to the floor: [tex]F cos \theta - \mu R = 0[/tex]
where
F is the push of the gardener
R is the normal reaction
m = 20 kg is the mass
g = 9.8 m/s^2 is the acceleration of gravity
[tex]\mu=0.18[/tex] is the coefficient of friction
[tex]\theta=37^{\circ}[/tex]
Solving for R,
[tex]R=mg-Fsin \theta[/tex]
Substituting into the other equation,
[tex]F cos \theta - \mu (mg-Fsin \theta) = 0\\F cos \theta - \mu mg + \mu F sin \theta = 0\\F(cos \theta+\mu sin \theta)=\mu mg\\F=\frac{\mu mg}{cos \theta + \mu sin \theta}=\frac{(0.18)(20)(9.8)}{cos 37^{\circ}+0.18(sin 37^{\circ})}=38.9 N[/tex]
And the power he must supply therefore is the product of this force and the speed:
[tex]P=Fv=(38.9)(1.5)=58.4 W[/tex]
The gardener has to apply to push force to move the lawnmower at a speed of 1.5 m/s is 59.41 Watts.
What is friction?
It is a force that opposes the motion of the body. It is given as the product of the normal force to the body and coefficient of friction between the surfaces.
A gardener pushes a 20 kg lawnmower whose handle is tilted up 37∘ above horizontal.
The lawnmower's coefficient of rolling friction is 0.18.
The force in the y-direction, we have
N = 20 × 9.81 - F sin 37°
N = 196.2 - 0.6 F ...(i)
The force in the x-direction, we have
F cos 37° = μN
0.8 F = 0.18N
Put the value of N in the above equation, we have
0.8 F = 0.18(196.2 - 0.6F)
0.8F = 34.596 - 0.108 F
F = 38.94 N
Then the power will be
P = F × v = 38.94 × 1.5 = 58.41 W
More about the friction link is given below.
https://brainly.com/question/13357196
