A 15 kg block lies on a smooth ramp that is inclined at 40 degrees to the ground.
a. determine the force that this blocks exerts in a direction perpendicular to the ramp.
b. what is the force, parallel to the inclined plane, needed to prevent the block from slipping?
To determine the force that the block exerts in a direction perpendicular to the ramp, you can use the formula:
Force perpendicular = Weight of the block × cos(θ)
where θ is the angle of the ramp (40 degrees) and Weight of the block = mass × gravity.
a. The weight of the block can be calculated as:
Weight of the block = mass × gravity = 15 kg × 9.8 m/s^2 = 147 N
Substituting the values into the formula:
Force perpendicular = 147 N × cos(40 degrees) ≈ 112.53 N
Therefore, the force that the block exerts in a direction perpendicular to the ramp is approximately 112.53 N.
b. To determine the force parallel to the inclined plane needed to prevent the block from slipping, you can use the formula:
Force parallel = Weight of the block × sin(θ)
Substituting the values:
Force parallel = 147 N × sin(40 degrees) ≈ 94.94 N
Therefore, the force parallel to the inclined plane needed to prevent the block from slipping is approximately 94.94 N.