a) The friction force can be calculated using the equation:
friction force = coefficient of friction * normal force
The normal force can be found by decomposing the weight of the block into two components: one perpendicular to the plane and one parallel to the plane. The component parallel to the plane is equal to mg*sin(30º), where m is the mass of the block and g is the acceleration due to gravity. Therefore, the normal force is equal to mg*cos(30º).
Plugging in the values, we get:
friction force = 0.3 * 2 kg * 9.8 m/s^2 * cos(30º)
friction force = 5.086 N
b) The acceleration of the block as it moves up the plane can be found using Newton's second law:
ΣF = ma
Where ΣF is the net force acting on the block. The net force is equal to the component of the weight of the block parallel to the plane minus the friction force. Therefore:
ΣF = mg*sin(30º) - friction force
ΣF = 2 kg * 9.8 m/s^2 * sin(30º) - 5.086 N
ΣF = 14.704 N - 5.086 N
ΣF = 9.618 N
Now, we can calculate the acceleration:
9.618 N = 2 kg * a
a = 4.809 m/s^2
c) The time it takes for the block to move up the plane can be found using the kinematic equation:
v^2 = u^2 + 2as
Where v is the final velocity (0 m/s), u is the initial velocity (22 m/s), a is the acceleration (4.809 m/s^2), and s is the distance traveled up the plane. The distance traveled up the plane can be found using trigonometry as:
s = d*sin(30º)
Plugging in the values, we get:
0 = (22 m/s)^2 + 2 * 4.809 m/s^2 * d * sin(30º)
d = 82.501 m
Now, we can find the time:
s = vt
82.501 m = 22 m/s * t
t = 3.75 s
Therefore, the block takes approximately 3.75 seconds to move up the plane.
A block having a mass of 2 kg is projected up a long 30º inclined plane with an initial velocity of 22 m/s The coefficient of friction between the block and the plane is 0.3.
a) Find the friction force acting on the block as it moves up the plane.
b) What is the acceleration of the block as it moves up the plane?
c) How long a time does the block move up the plane?
1 answer