A 280 N block rests on a 30° incline. (a) What is the normal force exerted by the incline on the
block? (b) What (static) friction force is needed to prevent the block from sliding down the
incline? (c) What is the minimum coefficient of static friction needed?
a. mg*cosTheta
b. gravity forced down the plane=mg*sinTheta
c. mg*cosTheta*mu=mgSinTheta
mu=tanTheta
a. 242.5N
b. 140N
c. 0.5
To find the answers to these questions, we can use some basic principles of physics and the concept of forces.
(a) The normal force is the force exerted perpendicular to the plane of the incline. It is the force that balances the weight of the object when it is at rest. In this case, the weight of the block is 280 N. To find the normal force, we need to find the component of the weight that acts perpendicular to the incline, which is given by:
Normal force = Weight * cos(angle)
Since the angle of the incline is 30°, we can calculate the normal force using:
Normal force = 280 N * cos(30°)
(b) To prevent the block from sliding down the incline, there must be a force of static friction that acts opposite to the direction of motion. The maximum force of static friction can be found using:
Force of static friction = coefficient of static friction * Normal force
(c) The coefficient of static friction is the ratio of the maximum force of static friction to the normal force. To find the minimum coefficient of static friction needed, we divide the maximum force of static friction by the normal force:
Minimum coefficient of static friction = Force of static friction / Normal force
Now we can calculate the answers to the questions using these formulas:
(a) Normal force = 280 N * cos(30°)
(b) Force of static friction = coefficient of static friction * Normal force
(c) Minimum coefficient of static friction = Force of static friction / Normal force
Note: Make sure to use the appropriate unit conversions if necessary.