When a horse pulls a 54 kg buggy down the road with a force of 56 N, the buggy hitch makes an angle of 25 degrees above the horizontal. If the force of friction on the buggy is 3 N, what is the buggy's acceleration? Report your answer to 2 decimal places. Do not include the units in your answer or the computer will mark the problem wrong.
the net force is 56cos25°-3 = 47.75N
F = ma, so a = 47.75N/54kg = 0.884 m/s^2
To find the buggy's acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force acting on the buggy is the force of the horse minus the force of friction.
1. Calculate the horizontal component of the force of the horse pulling the buggy:
The horizontal component can be found using the formula:
F_horizontal = F * cos(theta)
where F is the force of the horse (56 N) and theta is the angle (25 degrees).
F_horizontal = 56 * cos(25)
2. Calculate the net force acting on the buggy:
The net force is the horizontal component of the force of the horse minus the force of friction.
Net force = F_horizontal - force of friction
Net force = (56 * cos(25)) - 3
3. Calculate the acceleration of the buggy:
Use Newton's second law of motion to find the acceleration:
Net force = mass * acceleration
acceleration = Net force / mass
acceleration = (56 * cos(25)) - 3 / 54
4. Calculate the acceleration to 2 decimal places:
Use a calculator to find the value of the expression:
acceleration ≈ (56 * cos(25)) - 3 / 54 ≈ 0.72
Therefore, the buggy's acceleration is approximately 0.72.
To find the buggy's acceleration, we first need to calculate the net force acting on the buggy. The net force is the vector sum of all the forces acting on an object.
In this case, the forces acting on the buggy are the force of the horse pulling it and the force of friction opposing its motion. The force of the horse is given as 56 N at an angle of 25 degrees above the horizontal, and the force of friction is given as 3 N.
Since the force of the horse is not directly horizontal, we first need to find its horizontal and vertical components. The horizontal component can be calculated using the formula:
Horizontal component = Force of horse * cos(angle)
Substituting the given values, we get:
Horizontal component = 56 N * cos(25°)
Next, we can calculate the net force in the horizontal direction by subtracting the force of friction:
Net force in the horizontal direction = Horizontal component - Force of friction
Now that we have the net force in the horizontal direction, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force in the horizontal direction = Mass of buggy * Acceleration
Since the mass of the buggy is given as 54 kg, we can rearrange the equation to solve for acceleration:
Acceleration = Net force in the horizontal direction / Mass of buggy
Substituting the known values, we get:
Acceleration = (Horizontal component - Force of friction) / 54 kg
Now we can calculate the acceleration by substituting the values we obtained earlier:
Acceleration = (56 N * cos(25°) - 3 N) / 54 kg
Performing the calculations, the acceleration comes out to be approximately 1.02 m/s^2.