A block of mass 15kg rest on a horizontal floor ( coefficient of friction is 0.4)
(A) what force is required just to make de block move when (i) pulling horizontally (ii) pulling at an angle of 60 to the horizontal
(2) if the block is pulled with horizontal force of 50N, with what acceleration does it move. Take g=10m/s
Fnet>Fmk
Fmk=m*a*mk=(15kg)*(9.8m/s^2)*(0.4)=58.8N
Fnet>58.8N
@60 ° angle
58.8N=Fcos60
(58.8N/Cos60)=117.6=F
117.6 N < Fnet
Does it move when 50N is pulling it in the horizontal direction????
Yes
To find the force required to make the block move, we need to consider the force of friction acting on the block.
(A) (i) Pulling horizontally:
In this case, the force required to make the block move horizontally is equal to the force of static friction, as initially, the block is at rest on the floor.
The formula to calculate the force of friction is given by:
Frictional force = coefficient of friction * Normal force
The normal force is the force exerted by the floor on the block, and it is equal to the weight of the block, which is given by:
Normal force = mass * acceleration due to gravity
Plugging in the values, we get:
Normal force = 15 kg * 10 m/s^2 = 150 N
Frictional force = 0.4 * 150 N = 60 N
Therefore, a force of at least 60 N is required to make the block move horizontally.
(ii) Pulling at an angle of 60 degrees to the horizontal:
In this case, we need to resolve the force applied into its horizontal and vertical components.
The horizontal component of the force (F_horizontal) is given by:
F_horizontal = Force * cos(angle)
Plugging in the values, we get:
F_horizontal = 50 N * cos(60 degrees) = 25 N
Now, we can use the same formula to calculate the force of friction as before:
Frictional force = 0.4 * 150 N = 60 N
Since the force of friction is greater than the horizontal component of the force (60 N > 25 N), the block will not move in the direction of the applied force at this angle.
(2) If the block is pulled with a horizontal force of 50 N, the net force acting on the block in the horizontal direction is equal to the applied force minus the force of friction:
Net force = applied force - force of friction
Net force = 50 N - 60 N = -10 N
Since the net force is negative, the block will experience a deceleration in the opposite direction of the applied force.
To find the acceleration, we use Newton's second law of motion:
Net force = mass * acceleration
Plugging in the values, we get:
-10 N = 15 kg * acceleration
Solving for the acceleration, we get:
acceleration = -10 N / 15 kg = -0.67 m/s^2
Therefore, the block will move with a deceleration of 0.67 m/s^2 when pulled with a horizontal force of 50 N.