Sarah is pushing a 10 kg buggy and exerts a force of 100 N along the handle. If the handle is elevated at 37° to the horizontal, determine the component of the force that will move the buggy forward. If a frictional force of 60 N exists as she pushes it over a grass covered parkway, determine the acceleration of the buggy.
Fx = 100*Cos37 = 79.86 N.
Wb = m*g = 10kg * 9.8N/kg = 98 N. =
Weight of buggy.
a=(Fx-Fk)/m = (79.86-60)/10=1.99 m/s^2
To determine the component of the force that will move the buggy forward, we need to find the horizontal component of the force exerted by Sarah.
The horizontal component of the force can be found using the formula:
Force_horizontal = Force * cos(angle)
Here, the angle is the angle of elevation of the handle from the horizontal, which is given as 37°.
Substituting the values into the formula, we have:
Force_horizontal = 100 N * cos(37°)
Calculating this, we get:
Force_horizontal ≈ 100 N * 0.7986 ≈ 79.86 N
Therefore, the component of the force that will move the buggy forward is approximately 79.86 N.
Now, let's determine the acceleration of the buggy. We can use Newton's second law of motion:
Force_net = mass * acceleration
The net force acting on the buggy is the force exerted by Sarah minus the frictional force. So we have:
Force_net = Force_horizontal - Frictional force
Substituting the given values, we get:
Force_net = 79.86 N - 60 N
Calculating this, we find:
Force_net = 19.86 N
Now, we can find the acceleration of the buggy using Newton's second law:
Acceleration = Force_net / mass
Substituting the values, we get:
Acceleration = 19.86 N / 10 kg
Calculating this, we find:
Acceleration ≈ 1.986 m/s^2
Therefore, the acceleration of the buggy is approximately 1.986 m/s^2.