Question

An object with a mass of 4 kg is kept motionless on an inclined plane by a force parallel to the plane. The angle of the incline is 30°; the object is at a vertical height of 10 m above the bottom; friction is negligible. What is the value of the force in Newtons?
A) 4.0
B) 4.9
C) 9.8
D) 19.6
E) 39.2

Answer 1

Answer on Question #45041, Physics, Mechanics | Kinematics | Dynamics

An object with a mass of $4\mathrm{kg}$ is kept motionless on an inclined plane by a force parallel to the plane. The angle of the incline is $30{}^{\circ}$ ; the object is at a vertical height of $10\mathrm{m}$ above the bottom; friction is negligible. What is the value of the force in Newtons?

A) 4.0

B) 4.9

C) 9.8

D) 19.6

E) 39.2

Solution.

As the object is motionless, from the Newton's first law:

$$\vec {F} + m \vec {g} + \vec {N} = 0$$

In projection on $X$ axis:

$$\begin{array}{l} - F + m g \cdot \sin (\alpha) = 0 \\ = m g \cdot \sin (\alpha) \\ \end{array}$$

Numerically:

$$= 4 k \cdot 9. 8 \frac {m}{s ^ {2}} \cdot \sin (3 0 {}^ {\circ}) = 1 9. 6 N$$

Answer: D) $= 19.6N$

http://www.AssignmentExpert.com/