Question

Starting from rest, you pushed a 10.0 kg lawnmower a distance of 25 meters by applying a force of 75 N at an angle 35 degrees below horizontal, as shown below. Use work and energy principles to calculate how fast the lawn mower is moving (in m/s) at the end of the 25 meters.

Answer 1

The lawn mower is moving with a velocity of 17.53 m/s

Definition of Energy and Work

Energy is the ability to do work while Work is defined as the product of force and distance moved in the direction of the force. Both work and energy are measured in Joule (J)

Work = Force (F) × distance (d) = FdCosθ

With the above formula, we can obtain the energy used in pushing the lawn mower as illustrated below

From the question given above, the following data were obtained:

•Force (F) = 75 N

•Distance (d) = 25 m

•Angle (θ) = 35°

•Energy (E) =?

E = FdCosθ

E = 75 × 25 × Cos 35

E = 1535.91 J

Definition and Determination of the velocity

Velocity is the rate of change of displacement with time.

Velocity and energy are related according to the following equation:

E = ½ × mass (m) × square velocity (v²)

E = ½mv²

With the above formula, we can obtain the velocity of the lawn mower as follow

•Mass (m) = 10 Kg

•Energy (E) = 1535.91 J

•Velocity (v) =?

E = ½mv²

1535.91 = ½ × 10 × v²

1535.91 = 5 × v²

Divide both side by 5

v² = 1535.91 / 5

Take the square root of both side

v = √(1535.91 / 5)

v = 17.53 m/s

Thus, the lawn mower is moving with a velocity of 17.53 m/s

Learn more about energy:
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