What is the acceleration of a 2-kg cart placed on a frictionless ramp inclined at 20 degrees?
that would be 9.8 sin20°
oops. That's the force.
divide by mass for acceleration.
9.8 sin 20 is right as is :)
To find the acceleration of a cart placed on a frictionless ramp inclined at an angle, we can use the concept of the component of gravity along the incline.
The first step is to determine the force of gravity acting on the cart. The force of gravity is the product of the mass (m) of the cart and the acceleration due to gravity (g).
Force of gravity = mass × acceleration due to gravity
Given that the mass of the cart is 2 kg, we can calculate the force of gravity:
Force of gravity = 2 kg × 9.8 m/s^2 (acceleration due to gravity)
Next, we need to find the component of this force acting along the incline. This component can be determined by multiplying the force of gravity by the sine of the angle of the incline (20 degrees in this case).
Force along the incline = Force of gravity × sin(angle of incline)
Substituting the values, we get:
Force along the incline = (2 kg × 9.8 m/s^2) × sin(20 degrees)
This force along the incline represents the force that is responsible for the acceleration of the cart. It can be calculated as follows:
Force along the incline = mass × acceleration
Rearranging the equation, we can solve for acceleration:
Acceleration = Force along the incline / mass
Plugging in the values we calculated earlier:
Acceleration = [(2 kg × 9.8 m/s^2) × sin(20 degrees)] / 2 kg
Now, let's do the math:
Acceleration = (19.6 m/s^2 × 0.342) / 2 kg
Acceleration ≈ 3.362 m/s^2
Therefore, the acceleration of the 2 kg cart placed on a frictionless ramp inclined at 20 degrees is approximately 3.362 m/s^2.