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3 years ago

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A gardener pushes a 20 kg lawnmower whose handle is tilted up 37∘ above horizontal. The lawnmower's coefficient of rolling frict

ion is 0.18. How much power does the gardener have to supply to push the lawnmower at a constant speed of 1.5 m/s ? Assume his push is parallel to the handle.

1 answer:

e-lub [12.9K]3 years ago

7 0

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: $F sin \theta + R -mg =0$

- Parallel to the floor: $F cos \theta - \mu R = 0$

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

$\mu=0.18$ is the coefficient of friction

$\theta=37^{\circ}$

Solving for R,

$R=mg-Fsin \theta$

Substituting into the other equation,

$F cos \theta - \mu (mg-Fsin \theta) = 0\\F cos \theta - \mu mg + \mu F sin \theta = 0\\F(cos \theta+\mu sin \theta)=\mu mg\\F=\frac{\mu mg}{cos \theta + \mu sin \theta}=\frac{(0.18)(20)(9.8)}{cos 37^{\circ}+0.18(sin 37^{\circ})}=38.9 N$

And the power he must supply therefore is the product of this force and the speed:

$P=Fv=(38.9)(1.5)=58.4 W$

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b. The second runner

c. 4.20 meters

Explanation:

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The relative speed is used to compared the velocity of one object (V1) to another object (V2). To learn the Relative Velocity from the second runner to the first we do the following:

Relative Speed (Vr) = Second Runner Velocity (Vs) - First Runner Velocity (Vf)

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This means that the second runner is gaining 0.7 meter from the first runner each second.

b. To know which runner will gain the race, we need to keep in mind, that the seconds runner is 45 meter more away that the first runner from the goal. Knowing this, the winner will be the one that reach the goal on less time.

Because movement is constant, we can use the following equation:

Velocity (V) = Distance (D) / Time (T)

To get the time we do:

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T = (250 meters + 45 meters) / (4.20 m/s)

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Distance from goal (Dg) = Total Distance (D) - Distance travelled (Dt)

Where Total Distance (D) is 250 mts. And the distance travelled can be obtained by using the following equation.

Velocity (V) = Distance (D) / Time (T)

Searching for distance:

D = V / T.

D = (3.50 m/s) * 70.23 s

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Answer with Explanation:

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Answer:

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