Answer:
Step-by-step explanation:
a. To determine the amount of force needed to move the block up the incline at a constant speed, we need to find the force of gravity acting on the block and the component of that force that acts parallel to the incline.
The force of gravity acting on the block is:
Fg = m * g
where m is the mass of the block and g is the acceleration due to gravity. Assuming a standard acceleration due to gravity of 9.81 m/s^2, we have:
Fg = 30 N * 9.81 m/s^2 = 294.3 N
The component of the force of gravity acting parallel to the incline is:
Fp = Fg * sin(theta)
where theta is the angle of incline. Substituting the values we have, we get:
Fp = 294.3 N * sin(10°) = 51.2 N
Therefore, the amount of force needed to move the block up the incline at a constant speed is 51.2 Newtons.
b. To find the work done in moving the block 3.0 meters along the plane, we need to use the formula:
Work = Force * Distance * cos(theta)
where Force is the component of the force of gravity acting parallel to the incline, Distance is the displacement of the block along the plane, and theta is the angle between the force and the displacement.
Substituting the values we have, we get:
Work = 51.2 N * 3.0 m * cos(10°)
Work = 148.4 J
Therefore, the work done in moving the block 3.0 meters along the plane is 148.4 joules.