a horizontal force of 1.2kgf is applied to 1.5kgf of block which rest on surface such that it just begin to slide .if coefficient of friction is 0.3.find out acceleration
netforce= mass*a
pushing force- frictionforce= mass*a
Now what is kgf?
http://en.wikipedia.org/wiki/Kilogram-force Frankly, if I were you, I would work it in SI
To find the acceleration of the block, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Horizontal force applied (F) = 1.2 kgf
Mass of the block (m) = 1.5 kgf
Coefficient of friction (μ) = 0.3
First, convert the forces from kgf to Newtons (N) by multiplying by 9.8 m/s² (acceleration due to gravity):
Force (F) = 1.2 kgf × 9.8 m/s² = 11.76 N
Weight of the block (mg) = 1.5 kgf × 9.8 m/s² = 14.7 N
The maximum static friction force (fs max) can be found by multiplying the coefficient of friction (μ) with the normal force (N), which is the weight of the block (mg):
fs max = μN = 0.3 × 14.7 N = 4.41 N
Since the horizontal force (F) is greater than the maximum static friction force (fs max), the block will start to slide. In this case, the frictional force acting on the block will be equal to the kinetic friction force (fk), which is also the product of the coefficient of friction (μ) and the normal force (N).
fk = μN = 0.3 × 14.7 N = 4.41 N
Now, the net force (Fnet) acting on the block can be calculated by subtracting the frictional force (fk) from the applied force (F):
Fnet = F - fk = 11.76 N - 4.41 N = 7.35 N
Finally, we can calculate the acceleration (a) using Newton's second law of motion (Fnet = ma), rearranging the formula to solve for acceleration:
a = Fnet / m = 7.35 N / 1.5 kg = 4.9 m/s²
Therefore, the acceleration of the block is 4.9 m/s².
To find the acceleration of the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, we need to convert the given forces from kilogram-force (kgf) to Newtons (N). Since 1 kgf is approximately equal to 9.8 N, the given force of 1.2 kgf is equivalent to 1.2 × 9.8 = 11.76 N, and the force of the block's weight (1.5 kgf) is 1.5 × 9.8 = 14.7 N.
The force of friction can be calculated using the equation:
force of friction = coefficient of friction × normal force
The normal force is the force exerted by the surface on the block and is equal to the weight of the block (14.7 N) since the block is resting on a horizontal surface.
Now, substituting the given coefficient of friction of 0.3 into the equation, we get:
force of friction = 0.3 × 14.7 N = 4.41 N
To find the net force acting on the block, we subtract the force of friction from the applied force:
net force = applied force - force of friction = 11.76 N - 4.41 N = 7.35 N
Finally, using Newton's second law, we have:
net force = mass × acceleration
Rearranging the formula, we can solve for the acceleration:
acceleration = net force / mass = 7.35 N / 1.5 kg = 4.9 m/s²
Therefore, the acceleration of the block is 4.9 m/s².