A box of mass 0.385 kg slides down a very smooth (frictionless) ramp which is inclined at an angle of 56.6° above the horizontal. What is the acceleration of the box down the ramp?
The Sum of Forces going down the ramp is equal to mg*sin*(theta). Mass * Acceleration = mg*sin (theta). since the masses are equal for both sides of the equation, you can write the equation as acceleration = g* sin (theta). and sove for the acceleration.
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To find the acceleration of the box down the ramp, we can use the following formula:
Acceleration = (gravitational force parallel to the ramp) / (mass of the box)
The gravitational force parallel to the ramp can be calculated using the following formula:
Gravitational force parallel to the ramp = (mass of the box) * (gravitational acceleration) * (sine of the angle of inclination of the ramp)
Given that:
- mass of the box = 0.385 kg
- gravitational acceleration = 9.8 m/s^2
- angle of inclination of the ramp = 56.6°
Let's calculate the acceleration step by step:
Step 1: Calculate the gravitational force parallel to the ramp.
Gravitational force parallel to the ramp = (0.385 kg) * (9.8 m/s^2) * sin(56.6°)
Step 2: Calculate the acceleration.
Acceleration = Gravitational force parallel to the ramp / mass of the box
Now, let's plug the values into the formulas and calculate the acceleration:
Step 1: Gravitational force parallel to the ramp = (0.385 kg) * (9.8 m/s^2) * sin(56.6°)
Gravitational force parallel to the ramp = 0.385 * 9.8 * sin(56.6°) ≈ 3.77 N
Step 2: Acceleration = Gravitational force parallel to the ramp / mass of the box
Acceleration = 3.77 N / 0.385 kg ≈ 9.77 m/s^2
Therefore, the acceleration of the box down the ramp is approximately 9.77 m/s^2.
To find the acceleration of the box down the ramp, we can utilize Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the force acting on the box is the component of the weight force parallel to the incline, which can be determined using the equation:
Force = weight * sin(θ)
where weight is the gravitational force acting on the box and θ is the angle of the incline.
The weight force can be calculated as:
Weight = mass * gravitational acceleration
where the mass is given as 0.385 kg and the gravitational acceleration can be assumed as 9.8 m/s^2.
So, Weight = 0.385 kg * 9.8 m/s^2.
Now, let's substitute the values into the equation for force:
Force = 0.385 kg * 9.8 m/s^2 * sin(56.6°).
Next, we know that force equals mass multiplied by acceleration:
Force = mass * acceleration.
By equating these two expressions for force, we have:
0.385 kg * 9.8 m/s^2 * sin(56.6°) = 0.385 kg * acceleration.
Now let's solve for acceleration:
acceleration = (0.385 kg * 9.8 m/s^2 * sin(56.6°)) / 0.385 kg.
By canceling out the unit of mass, we get:
acceleration = 9.8 m/s^2 * sin(56.6°).
Evaluating this expression, we can find the acceleration of the box down the ramp.