Can someone walk me through how to work this?
A block is being pushed up a frictionless incline by an applied horizontal force, F=12.7N. (The angle is θ = 23.80° and the mass is 1.70kg.
a) How many forces are acting on the block?
b) How many of those forces are along the vertical?
c) How many of those forces are perpendicular to the incline?
d) What is the magnitude in m/s2 of the resulting acceleration of the block?
Use 9.8 N/kg for g.
To answer these questions, we need to break down the problem and analyze the forces acting on the block. Let's walk through each question step by step:
a) How many forces are acting on the block?
To determine the number of forces acting on the block, we need to consider the forces involved in the given situation. In this case, we have the following forces:
1. Applied horizontal force (F) of 12.7N: This force is pushing the block up the incline.
2. The force of gravity (weight): This force is pulling the block downwards.
3. Normal force: This force is exerted perpendicular to the incline surface.
So, there are three forces acting on the block: the applied force, the force of gravity, and the normal force.
b) How many of those forces are along the vertical?
Out of the three forces mentioned above, only the force of gravity (weight) acts along the vertical direction. The applied force and normal force act in horizontal and perpendicular directions, respectively.
c) How many of those forces are perpendicular to the incline?
The only force that acts perpendicular to the incline surface is the normal force. The force of gravity and the applied force are not perpendicular to the incline.
d) What is the magnitude in m/s2 of the resulting acceleration of the block?
To find the acceleration, we need to consider the net force acting on the block and apply Newton's second law: F = ma. Since the incline is frictionless, the force of friction is zero.
The net force acting on the block can be determined by resolving the forces into the direction of motion and perpendicular to it. The force of gravity has two components: one along the incline and one perpendicular to it.
The force acting along the incline (parallel to the force applied) can be calculated by F_parallel = m * g * sin(θ), where θ is the angle of the incline.
Plugging in the values, we get:
F_parallel = 1.70 kg * 9.8 N/kg * sin(23.80°)
Next, we calculate the net force along the incline:
Net force along the incline = F_parallel - F_applied
Finally, we can calculate the acceleration using Newton's second law:
a = Net force along the incline / mass of the block
Plugging in the values we have calculated, we can find the magnitude of the resulting acceleration in m/s².