Answer:
a = 3.27 m/s²
F = 32.7 N
Explanation:
Draw a free body diagram. There are three forces:
Weight force mg pulling straight down.
Normal force N pushing perpendicular to the slope.
Friction force F pushing parallel up the slope.
Sum of forces in the parallel direction:
∑F = ma
mg sin θ − F = ma
Sum of torques about the cylinder's axis:
∑τ = Iα
Fr = ½ mr²α
F = ½ mrα
Since the cylinder rolls without slipping, a = αr. Substituting:
F = ½ ma
Two equations, two unknowns (a and F). Substituting the second equation into the first:
mg sin θ − ½ ma = ma
Multiply both sides by 2/m:
2g sin θ − a = 2a
Solve for a:
2g sin θ = 3a
a = ⅔ g sin θ
a = ⅔ (9.8 m/s²) (sin 30°)
a = 3.27 m/s²
Solving for F:
F = ½ ma
F = ½ (20 kg) (3.27 m/s²)
F = 32.7 N
Answer:
a). 1.218 m/s
b). R=2.8
Explanation:
Momentum of the motion the first part of the motion have a momentum that is:
The final momentum is the motion before the action so:
a).
b).
kinetic energy
Kinetic energy after
Kinetic energy before
Ratio =
By non-contact forces (e.g. gravitational force and electric force)
Explanation:
In order for an object to exert a force on another object, the two object can also be not touching each other. In fact, there exist some non-contact forces in nature.
Concerning macroscopic objects, the two main non-contact forces acting between objects are:
- The gravitational force: this force is exerted between every object that has mass. It is always attractive, and its magnitude is given by
where
is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between them
- The electric force: this force is exerted between objects that have electric charge. It can be either attractive or repulsive, and its magnitude is given by
where:
is the Coulomb's constant
are the two charges
r is the separation between the two charges
Learn more aboit gravitational and electric force:
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