A woman pushes a lawn mower with a con-
stant force of 112 Newtons at an angle of
37degrees with respect to the horizontal. The lawn mower moves at a speed of 20 cm/sec.
What is her power output? (1 hp = 746
Watts)
Fp = Fh = 112cos37 = 89.48N = Force parallel to the plane.
Po = Fp*V = 89.48 * 0.2m/s = 17.9W.
hp = Po/746 = 17.9 / 746 = 0.024.
To find the power output, we first need to calculate the work done by the woman in pushing the lawn mower.
Work (W) is defined as the product of force (F) and displacement (d) in the direction of the force. In this case, the force is acting at an angle with respect to the horizontal, so we need to consider the component of force in the horizontal direction.
The horizontal component of the force can be found using trigonometry. The equation is:
F_horizontal = F * cos(angle)
where F is the given force of 112 Newtons and angle is the given angle of 37 degrees.
Plugging in the values:
F_horizontal = 112 N * cos(37 degrees)
Next, we need to calculate the displacement in the horizontal direction. The speed of the lawn mower is given as 20 cm/sec. Recall that speed is the magnitude of velocity, and velocity is the rate of change of displacement. Therefore, to find the displacement, we need to multiply the speed by the time interval.
d = speed * time
Since the time is not given, we cannot directly calculate the displacement. However, we can work with the given values to find the time it takes for the lawn mower to move a certain distance. Let's assume that the distance moved by the lawn mower is 1 meter.
d = 1 m
speed = 20 cm/sec = 0.20 m/sec
Plugging in these values and rearranging the equation:
time = d / speed = 1 m / 0.20 m/sec = 5 sec
Now that we have the time, we can calculate the displacement:
d = speed * time = 0.20 m/sec * 5 sec = 1 meter
Finally, we can calculate the work done:
W = F_horizontal * d
Plugging in the values:
W = 112 N * cos(37 degrees) * 1 m
The angle here is given in degrees, but trigonometric functions typically work with radians. So, we need to convert the angle to radians:
angle_radians = angle_degrees * (pi / 180)
Plugging in the value:
angle_radians = 37 degrees * (pi / 180)
Now, we can calculate the work:
W = 112 N * cos(37 degrees * (pi / 180)) * 1 m
The power output (P) is defined as the rate at which work is done. It can be calculated using the formula:
P = W / t
where t is the time interval. We already calculated the time to be 5 seconds, so we can substitute that into the formula:
P = W / 5 sec
Lastly, since the question asks for the power output in horsepower, we need to convert the final answer from watts to horsepower using the given conversion factor:
1 hp = 746 Watts
Therefore, the power output can be calculated as:
P_hp = P / 746
Plugging in the values and solving the equations will give us the final answer.
To find the power output of the woman pushing the lawn mower, we need to use the formula:
Power = Force × Velocity
First, we need to calculate the horizontal and vertical components of the force applied.
Horizontal component of the force = Force × cos(angle)
Vertical component of the force = Force × sin(angle)
Given:
Force = 112 Newtons
Angle = 37 degrees
Velocity = 20 cm/sec
We convert the velocity from cm/sec to m/sec:
20 cm/sec = 0.2 m/sec
Let's calculate the horizontal and vertical components of the force:
Horizontal component of the force = 112 N × cos(37 degrees)
Vertical component of the force = 112 N × sin(37 degrees)
Using a calculator:
Horizontal component of the force ≈ 89.89 N
Vertical component of the force ≈ 67.82 N
Now, let's calculate the power as:
Power = (horizontal component of the force) × (velocity)
Power = 89.89 N × 0.2 m/sec
Power ≈ 17.978 W
To convert from watts to horsepower, we divide the power in watts by 746 (1 hp = 746 W):
Power ≈ 17.978 W ÷ 746
Power ≈ 0.0241 hp
Therefore, the woman's power output is approximately 0.0241 horsepower.