A toy sled with a mass of 1.0 kg is sliding down a ramp that makes an angle of 25° with the
ground. The coefficient of kinetic friction between the toy sled and the ramp is 0.25.
4. In a coordinate system where the x-axis is parallel to the ramp and the y-axis is perpendicular to
the ramp, what are the components of the toy sled’s weight?
5. In a coordinate system where the x-axis is parallel to the ground and the y-axis is perpendicular to
the ground, what are the component’s of the toy sled’s weight?
rgtge
No. do not mix sodium hydroxide and sulfuric acid. :3
4. In a coordinate system where the x-axis is parallel to the ramp and the y-axis is perpendicular to the ramp, the weight of the toy sled can be broken down into two components:
- The component of the weight along the x-axis (parallel to the ramp) is given by Wx = mg sinθ, where m is the mass of the sled and g is the acceleration due to gravity (approximated as 9.8 m/s²). In this case, θ is the angle the ramp makes with the ground, which is 25°. Therefore, the x-component of the weight would be Wx = (1.0 kg)(9.8 m/s²) sin(25°).
- The component of the weight along the y-axis (perpendicular to the ramp) is given by Wy = mg cosθ. Similar to the previous step, m is the mass of the sled, g is the acceleration due to gravity, and θ is the angle the ramp makes with the ground. Thus, Wy = (1.0 kg)(9.8 m/s²) cos(25°).
5. In a coordinate system where the x-axis is parallel to the ground and the y-axis is perpendicular to the ground, the weight of the sled can be broken down into two components:
- The component of the weight along the x-axis (parallel to the ground) would be the same as the weight of the sled since the toy sled is already on the ground and the x-axis is parallel to it. Therefore, the x-component of the weight is Wx = mg.
- The component of the weight along the y-axis (perpendicular to the ground) would be zero since the sled is on the ground, and there is no vertical acceleration acting on it. Therefore, Wy = 0.
To find the components of the toy sled's weight in different coordinate systems, we need to break down the weight vector into its x and y components.
First, let's consider the coordinate system where the x-axis is parallel to the ramp and the y-axis is perpendicular to the ramp.
4. In this coordinate system, the weight vector of the toy sled can be split into two components: one parallel to the ramp (x-axis) and one perpendicular to the ramp (y-axis).
The weight vector can be represented as W = mg, where "m" is the mass of the sled and "g" is the acceleration due to gravity (approximately 9.8 m/s²).
To find the component of weight parallel to the ramp (x-axis), we can use trigonometry. The weight component parallel to the ramp can be calculated as Wx = W * sin(θ), where θ is the angle of the ramp with the ground.
In this case, the angle of the ramp is 25°, so Wx = mg * sin(25°).
To find the weight component perpendicular to the ramp (y-axis), we can also use trigonometry. The weight component perpendicular to the ramp can be calculated as Wy = W * cos(θ), where θ is the angle of the ramp with the ground.
In this case, the angle of the ramp is 25°, so Wy = mg * cos(25°).
Now, let's consider the coordinate system where the x-axis is parallel to the ground and the y-axis is perpendicular to the ground.
5. In this coordinate system, the weight vector of the toy sled can be split into two components: one parallel to the ground (x-axis) and one perpendicular to the ground (y-axis).
To find the component of weight parallel to the ground (x-axis), it remains the same as Wx = mg * sin(θ) since the angle of the ramp with the ground is the same.
To find the weight component perpendicular to the ground (y-axis), it becomes Wy = mg * cos(θ), where θ is the angle of the ramp with the ground.
Considering the angle of the ramp with the ground is 25°, the weight component perpendicular to the ground can be calculated as Wy = mg * cos(25°).
By applying these formulas, you can calculate the components of the toy sled's weight in both coordinate systems.